Lesson 1A: Geometric Notation Name: Use correct notation when referring to lines, segments, rays, and angles. 1. Lines P A C D Q E F G H I a) Draw a line through points A and. What is one symbol or name for it? b) Draw a line through points C and D. Write a symbol for it. c) Are points E, F, and D collinear or not collinear? Why? d) Are points G, H, and I collinear or not collinear? Why? e) Draw PQ. Does it look like it will ever intersect A? f) What is the term for lines like PQ and A? Unit 1 Constructions and Transformations 1
2. Rays Q S T P C A W O X a) Draw a ray that starts at point P and passes through point Q. Which end does the arrow go on? How do we name it? b) Draw ST. What is its initial point? c) Draw A and AC. What do they have in common? d) Draw rays OX and OW. What is special about them? What are they called? e) Points W, O, and X are. f) Name 3 points that are not collinear. g) Since all the points lie in the same plane, they are called. Unit 1 Constructions and Transformations 2
3. Segments P C D F S E H G a) Draw a line segment that has endpoints C and D. How do we name it? b) DrawEF,EG,FG, and FH. Use a ruler! c) Segments FH and EG are segments. d) Points E, H, and G are. e) Draw PS. Mark its midpoint and label it M. f) Name 3 points that are not collinear. Unit 1 Constructions and Transformations 3
4. Your turn! Use a ruler to draw the lines, rays, and segments listed below. You will need 4 colored pencils. W C Z A D K R T L P Q S V M O N H E X G F Y a) Use the 1 st colored pencil to draw lines A,CD, EF and GH. Don t forget to add arrows! b) Use your 2 nd colored pencil to draw segments XW,YZ,WZ and XY. c) Use colored pencil #3 to draw these rays: KL, NO, PK, MN, OP and LM. d) Finish the diagram by using colored pencil #4 to draw segmentsqr,tv,rs andts. Done! Unit 1 Constructions and Transformations 4
5. An angle is formed when 2 different rays share the same initial point. The rays are called the sides of the angle and their initial point is called the vertex. When naming an angle, the name of the vertex always goes in the middle. Here are 3 names for the angle on the right: P Side Q Side Vertex R 6. Record the names of the sides and vertices of the angles below. Are the angles acute, obtuse, right, or straight? a) b) c) d) F H A W C X Y G S K R Sides: Vertex: Type: Sides: Vertex: Type: Sides: Vertex: Type: Sides: Vertex: Type: 7. Write 3 names for each of the angles below. C M T A S K P R H N Unit 1 Constructions and Transformations 5 O
8. Write at least 2 names for the marked angles in each figure. a) b) Q P A C O M N c) d) P Q E S A G R T C H D F 9. Fill in the boxes. Use correct notation! a) Name a point. b) Name a line segment. c) Name a ray. d) Name a pair of parallel lines. e) Name a pair of perpendicular lines. f) Name an acute angle. g) Name an obtuse angle. h) Name a right angle. Unit 1 Constructions and Transformations 6
10. The names of several different types of geometric objects are given below. Find an example of each one of them and write its name on the blank. You must use correct notation! a) Line: b) Ray: P T c) Segment: d) Angle: Q R S e) Triangle: 11. Name 4 different segments and 2 different angles. E G Segments: F Angles: D H 12. Name 2 different lines and 2 different segments C Lines: A Segments: D Unit 1 Constructions and Transformations 7
13. Take a look at the figure below. C X Y D A Z a) Name 2 rays. b) Name 2 acute angles. c) Name two obtuse angles. d) Name 2 segments. 14. a) Name a line. H S b) Name a segment. c) Name two different rays. Unit 1 Constructions and Transformations 8
Lesson 2A Midpoint Exploration Develop a formula for the midpoint of a line segment in the coordinate plane. 1. Plot the given numbers on the number line. Find their average and plot it too. a) 12 and 26 b) 15 and 23 Name: c) 16 and 33 d) 125 and 175 2. Find the midpoint of the following segments. a) b) c) Midpoint: Midpoint: d) Midpoint: Midpoint: 3. Try these! a) b) 24 40 31 37 Midpoint: Midpoint: 4. What s the secret? How can you calculate the midpoint if you know the endpoints? Unit 1 Constructions and Transformations 1
5. Let s go 2-dimensional! Find the midpoint of the following segments. a) b) Midpoint: Midpoint: c) d) ( 2,7) ( 8,3) Midpoint: Midpoint: 6. What s the secret for finding the midpoint in 2-dimensions? How can the midpoint be found from the coordinates of the endpoints? 7. Find the midpoint for the following pairs of points. a) A 17,12 and 39,28 b) C 1,13 and 9,14 Unit 1 Constructions and Transformations 2
Lesson 2 The Midpoint Formula Name: Use the Midpoint Formula to find the midpoint of line segments in the coordinate plane. 1. Locating Midpoints A C D a) Mark the midpoint of each side of the quadrilateral. b) Use a ruler to connect the midpoints in clockwise order. Shade the new quadrilateral that you get. c) What kind of quadrilateral did you shade? 2. Find the midpoint of each pair of points. 9,14 13,22 3, 6 a) A and b) Q and R 11,2 c) T 40,16 and W 20,28 d) X 4, 10 and Z 12, 2 e) F 2.5,4.8 and G 1.3,5.2 f) S 78, 24 and T 103, 42 Unit 1 Constructions and Transformations 1
3. Find the midpoint of FH. y H(12,18) 4. What is the midpoint of PT? P(-4,5) y F(2,6) x x T(6,-3) Midpoint: 5. Find the midpoint of A. Midpoint: 6. Segment CD has been graphed below. Find the midpoint of this segment. D A C Midpoint: Midpoint: 7. Consider the triangle below. a) Find the midpoint of side A : b) Find the midpoint of side C : A C c) Find the midpoint of side AC : d) Connect the midpoints of all three sides. What kind of triangles do we get? How are they related to each other? Unit 1 Constructions and Transformations 2
Lesson 3A - Perpendicular isector Construction Name: 1. Construct the perpendicular bisectors of the segments below. I C S T Pictorial summary of steps: 1. 2. 3. 4. E P Q P Q Q P M Q P Unit 1 Constructions and Transformations 1
2. Construct the perpendicular bisectors of the segments below. Unit 1 Constructions and Transformations 2
3. Constructions with Perpendicular Segments You ve got a point, P. You ve got a line, m. Construct a line that is perpendicular to P and passes through line m. P m m P m P m P Unit 1 Constructions and Transformations 3
4. Altitudes Construct the altitude that passes through vertex A. A C A C A C Unit 1 Constructions and Transformations 4
Lesson 3 More Constructions Name: A compass and straightedge can be used to construct a copy of a given line segment. 1. First, let s practice what we know already. Construct the perpendicular bisectors of the segments below. Pictorial summary of steps: 1. 2. 3. 4. P Q P Q Q P M Q P Unit 1 Constructions and Transformations
2. Constructing a Copy of a Line Segment Use a compass and straightedge to construct a segment whose length is A+CD. a) A C D b) A C D c) A C D Unit 1 Constructions and Transformations
Lesson 4A: The Pythagorean Theorem Name: My theorem about right triangles is one of the most famous mathematical theorems in the world. Do you know what it is??? c a b ---------------------------------- 1. Find the length of the hypotenuse for each of the triangles below. a) b) c) 6 c c 12 c 16 7 8 5 d) e) f) 14 2 8 c 9 c c 3 20 Unit 1 Constructions and Transformations 1
2. Practice! Use the Pythagorean Theorem to find the missing sides. e careful! This time the missing side is a leg of the right triangle, not the hypotenuse! a) b) 45? 35 37? 117 c)? 41 40 d) e) 514 45? 64 53? Unit 1 Constructions and Transformations 2
3. I see dots! Draw a right triangle that has legs 6 units long and 10 units long Find the length of the hypotenuse and the perimeter of the triangle. Length of Hypotenuse: Perimeter: 4. Diagonals. The rectangle below has 2 diagonals. Draw 1 of them. Use the Pythagorean Theorem to find the length of the diagonal. 32 24 Unit 1 Constructions and Transformations 3
Let s put my theorem to work!!! I m so excited, I almost feel alive again!!! We re going to need it!!! 5. Use the Pythagorean Theorem to find the perimeter of the triangle below. A Find the lengths of the following sides. Use right triangles! a) Side A b) Side AC c) Side C C d) What s the perimeter? P= Unit 1 Constructions and Transformations 4
6. Use the Pythagorean Theorem to find the perimeter of the triangle below. A Find the lengths of the following sides. Use right triangles! a) Side A b) Side AC c) Side C C d) What s the perimeter? P= Unit 1 Constructions and Transformations 5
Problem #7: Distances Use the Pythagorean Theorem to find the distances between the given pairs of points. a) Points A and y 10 F 9 8 D 7 b) Points D and C 6 5 E 4 A 3 2 1 c) Points E and F -2-1 0 1 2 3 4 5 6-1 -2 d) Points D and F 7 8 9 10 x C Check this out: Distance = x x y y 2 2 2 1 2 1 3) Label the following coordinates as x, x, y, or y. Use the formula to compute the distance 1 2 1 2 between the points. a) A(4,15) and (6, 27) b) C(-2,8) and D(4, 13) c) E(6,-4) and F(10,-1) Unit 1 Constructions and Transformations 6
Lesson 5A - Angle Measurement Name: You will definitely need one of these angle measuring thingies!!! 1. Use your protractor to measure the ten angles below. a) b) 1 2 m 1= m 2 = c) d) 3 4 m 3= m 4 = Unit 1 Constructions and Transformations 1
e) f) 6 5 m 5= m 6= g) h) 7 8 m 7 = g) m 8= h) 9 10 m 9 = m 10 = Unit 1 Constructions and Transformations 2
2. Now, use your protractor to make an angle with the given measurement. a) 60 b) 125 c) 35 d) 90 e) 100 f) 155 g) 180 Unit 1 Constructions and Transformations 3
5. Find the angle measurements. m 1= m 2 = 1 2 4 3 m 3 = m 4 = 6. The lower part of the John Hancock building is shown below. Measure angles 1 and 2. 1 2 m 1= m 2 = Unit 1 Constructions and Transformations 4
Lesson 5 isecting and Copying Angles Name: Use a compass and straightedge to construct angle bisectors and copies 1. Use a compass and straightedge to construct the angle bisectors of the angles shown below. Pictorial summary of steps: 1. Start with the original angle. 2. Draw an arc and mark where it intersects the angle. 3. Use the two new points to draw 2 more arcs. 4. Draw a ray through where the two arcs intersect. Unit 1 Constructions and Transformations 1
2. Construct the angle bisectors. 3. Construct the angle bisector of PQR in the figure below. Q P R Unit 1 Constructions and Transformations 2
Last Construction: Copying Angles. 4. Copy the angles below by using only a compass and a straight edge. 2 1 3 Pictorial summary of steps: 1. Draw a ray. 2. Construct an arc as shown and on original angle. 3. Use original angle to determine the radius for the second arc. 4. Draw a second ray through the point of intersection. Unit 1 Constructions and Transformations 3
5. Copy the angles below. Use only a compass and a straightedge. Unit 1 Constructions and Transformations 4
Lesson 6A - Algebraic Rules for Transformations Apply algebraic rules for transformations and describe their effect. Transformation #1: ( x, y) ( x 7, y) 6 y Name: 5 4 3 2 1-6 -5-4 -3-2 -1 1 2 3 4 5 6 x -1-2 -3-4 -5-6 a) Use Colored Pencil #1 to plot and label the following points. Connect them to form a triangle. A( -5,-2) (-3,3) C(-1,-3) b) Get 3 new points by applying the transformation to the 3 original points listed above. Old New c) Use Colored Pencil #2 to plot and label the new points. Connect them to form a new figure. d) Describe how the original figure was changed by the transformation. Education Development Center, Inc., 2009 1
Transformation #2: ( x, y) ( x, y 6) y 6 5 4 3 2 1-6 -5-4 -3-2 -1 1 2 3 4 5 6 x -1-2 -3-4 -5-6 a) Use Colored Pencil #1 to plot and label the following points. Connect them to form a parallelogram. A( -3,-3) (-2,-5) C(5,-5) D(4,-3) b) Get 4 new points by applying the transformation to the 4 points listed above. Old New c) Use Colored Pencil #2 to plot and label the new points. Connect them to form a new figure. d) Describe how the original figure was changed by the transformation. Education Development Center, Inc., 2009 2
Transformation #3: ( x, y) (3 x,2 y) 6 y 5 4 3 2 1-6 -5-4 -3-2 -1 1 2 3 4 5 6 x -1-2 -3-4 -5-6 a) Use Colored Pencil #1 to plot and label the following points. Connect them to form a triangle. A( -2,-2) (2,-3) C(0,2) b) Get 3 new points by applying the transformation to the 3 points listed above. Old New c) Use Colored Pencil #2 to plot and label the new points. Connect them to form a new figure. d) Describe how the original figure was changed by the transformation. Education Development Center, Inc., 2009 3
Transformation #4: ( x, y) ( x, y) 6 y 5 4 3 2 1-6 -5-4 -3-2 -1 1 2 3 4 5 6 x -1-2 -3-4 -5-6 a) Use Colored Pencil #1 to plot and label the following points. Connect them to form a trapezoid. A( -4,1) (-2,3) C(2,2) D(4,1) b) Get 4 new points by applying the transformation to the 4 points listed above. Old New c) Use Colored Pencil #2 to plot and label the new points. Connect them to form a new figure. d) Describe how the original figure was changed by the transformation. Education Development Center, Inc., 2009 4
5. This one has a beautiful parabola 1. The nine marked points lie on a curve called a parabola. OLD NEW a) Record the coordinates of these points in the OLD column of the table. b) Apply the following transformation to all of the old points. Record the new coordinates in the NEW column. ( x, y) ( x 10,18 y) c) Plot the new points and draw a new parabola. Education Development Center, Inc., 2009 5
Problem #6: Transformation Rule: ( x, y) ( x 5, y 7) y 6 5 4 3 2 1-6 -5-4 -3-2 -1 1 2 3 4 5 6 x -1-2 -3-4 -5-6 a) Plot and label the following points. Connect them to form a polygon. A( -5,4) (-2,4) C(-2,5) D(-1,3) E(-2,1) F(-2,2) G(-5,2) b) Get 7 new points by applying the transformation to the 7 points listed above. Old New c) Plot your new set of points. Connect them to form a new figure. Education Development Center, Inc., 2009 6
Lesson 7A What s This? acktracking? Name: 1. Solve!!! (Now would be a good time to backtrack ) a) 4x 39 33 b) 6x 100 52 c) 3 x 19 21 d) x 2 4 4 x x e) 9 2 f) 94 41 6 17 g) x 9 x 14 2 h) 16 20 6 Scrambled Answers: 2295 26 18-66 -8 134-6 23
2. Complete the grid below. Do one column at a time. (For example, for the first column evaluate all the expressions for when x=7. For the second column, evaluate all the expressions for x=-9 ) x 7-9 x 16 19 2 x 16 22 6 2 x 16 20 36 Workspace:
Unit 1: Lesson 7 Name: More Advanced Equations 6x 28 125 3x What do you do if the variable x is on both sides of the equation? 1. Solve the following multi-step equations. a) 9x 169 6x 53 b) 17 6x 25 4x c) 7x 109 6x 200 d) 3x 11 50 2x e) 5x 3.5 10 x f) 7 19 40 4 x x Scrambled Solutions: 1.625 74 28 7.8-4 -7 1
2. Oh No! Help!!! I see variables on both sides of these equations!!! Use a basic move to cancel one of the x terms. Finish solving! a) 13x 40 4x 59 b) 7x 30 10 2x c) 4x 37 3x 100 d) 2x 114 4x 36 e) 4x 23 2x 7 f) 7x 50 26 3x g) 6x 41 4x 169 h) 5x 12 2x 9 Scrambled Answers: 25-6 9 7 11 15-4 21 2
3. Equal Perimeters For each pair of figures below, determine the value of x that would make their perimeters equal to each other. a) b) x x+6 3x 28 3 16 Workspace: x Workspace: Answer: c) Answer: d) 14 20 24 14 x+4 x+2 2x 10 x+2 Workspace: Workspace: Answer: Answer: 3
Quick!!! Emergency Review! 4. Distribute! a) 4(3x 10) b) 3(4x 10) c) 3(16 4 x ) d) 2(17 3 x) e) 3( 4x 5) f) 4(7 2 x) g) 5( 12x 20) h) 6( 2x 4) 5. Distribute and Combine Like Terms. a) 7 3x 10 4 2x 12 b) 3 2x 9 2 4 5x 6. Rectangles and Areas x 16 7 6x+10 Write an expression for the total area of the rectangles. Simplify it by distributing and combining like terms. Simplified Expression for the total area: 4
7. Solve by acktracking or with asic Moves a) 18a 35 181 b) 14b 31 283 8. Cancel one of the variable terms and then use backtracking to solve these equations. a) 20c 25 305 6c b) 6d 15 4d 375 9. efore backtracking, sometimes you need to distribute and combine like terms! a) 4 2x 31 100 160 b) x x 3 6 2 4 80 5
10. Solve! Remember to simplify both sides as much as possible first. Check the fishbowl for answers! a) 4 x 32 2 3x 20 378 b) 4 x 7 2 x 18 42 c) x x 3 6 18 78 4 5 12 36 d) x 18 2 4 3x 60 e) 1 4 16 20 100 2 x 28-10 6 29 17 6
11. Equal Areas Determine the value of x that would make the areas of the following rectangles equal. a) b) 2 3 x+12 x+17 Go for it!!! 5 x+4 x-1 Workspace: 4 Workspace: Solution: Solution: 7
12. Three More. If you can do these, you ve got this mastered!!! a) 3x 5x 6 18 2x 28 b) 124 8x 3x 2x 16 8x 20 10x 5x c) 6x 3 4 7x 25 2 x 19 Solution: Solution: Solution: Let s chill!!! 8
Geometry Name E U2c0o1V6a NKWuStOaD TSYobfjt`wAatryez glolhc].h k OAIlrl_ [r[ixgihitksw FrkebswejrUvTe[db. Lesson 7C - Segment Addition Problems Find the length indicated. Date 1) Find GH 2) Find CD F x - 2 2x - 6 G H C 3x 2x + 2 D E 13 12 3) Find KJ 4) Find LM K -1 + 4x 7x J I L 2x - 3 4 M N 10 x + 4 j u2m0d1p6w tkiu[tkat ESpoNfstJwea\rHet YLILwCf.^ r tanlrla prpirgjhutpsn lrgetsresrkvjeidw.e J omha_dmee Uwmiytbhj WIon[f[iGnWiztje[ igfeiokmkewtur\yo. -1- Worksheet by Kuta Software LLC
5) Find HG 6) Find PQ I 5 2x - 10 H G P x - 3 Q x R x + 1 11 7) Find C 8) Find UV A 6 x + 1 C T 6 2x + 15 V U 3x - 1 x + 14 k x2r0l16[ YKkubt_ad fsooafmtnwlahrte] NLxLqCr.o S RAIlvlR Erhiggehdtisg srqe_sieyr[vxeudz.w J HMLaydoeH ewpiut[hk IIKnwfEiinriztVeq CGCeyoTmPehttrVyu. -2- Worksheet by Kuta Software LLC
Geometry N z2i0d1r4f jkpujthad ISgoZfztAwWavrzey klilucg.z \ WAIlslo FrbiCgghgtmsY \rbeyste`ravle]dd. Translations Name Date Period Graph the image of the figure using the transformation given. 1) translation: 5 units up 2) translation: 6 units left and 5 units up y y Y x E x G N A P 3) translation: 7 units right and 3 units down y 4) translation: 3 units right and 1 unit up y X S N Q x x Y b D2z0G1f4O vkcudtean FS_oOf^tnwzaUrzeE zl^l^co.q c eakljlv Ar^ingVhhtxsy IrWeLsNesrsvheJdz.S p `MyaodYeQ Jw]iItHhG qi^nkfqifnsi^tsek GueioWmZedtHrayQ. -1- Worksheet by Kuta Software LLC
5) translation: 4 units left S(1, -1), W(5, 1), J(3, -3) y 6) translation: 5 units left and 3 units down K(0, 0), I(0, 3), U(4, 1) y x x 7) translation: 2 units right and 6 units up G(-3, -2), S(1, -1), I(-1, -5) y 8) translation: 4 units right and 6 units up J(-3, -3), C(-2, -1), (0, -1), I(1, -4) y x x r b2i0i1t4o [KTuKtmaL ws`opfat]wkakrkeo nlmlgck.z FAlmln DrjiWghhwt^so vr]ezsfevrsvjeedh.f H DM[aqdie[ jwsiet]hn rimnzfpipn`ietqe ZGtenobmCe_tArnyI. -2- Worksheet by Kuta Software LLC
Geometry ack to Translations! Name: Mr. Miller (WU 9-28-16) 1. In the figure below, triangle AC was translated to produce triangle A C. Draw the translation vector from A to A, to, and from C to C. A C A C b) Write the component form of the vector: c) Write a rule for this transformation: 2. Draw the image of triangle AC after a translation along v. A C v
3. Draw the preimage and image of the triangle under the given translation. Triangle: P(1,-4); Q(4,-4); R(4,-2) Vector: 5, 3 b) Write a rule for this translation: 4. The coordinates of a quadrilateral are given below. What are the coordinates of its image after applying the vector 7, 2? Quadrilateral: A(-2,1); (2,2); C(4,-1); D(1,-4) A = = C = D = b) Write a rule for this translation:
Lesson 9A Introduction to Reflections Part 1: Horizontal and Vertical Lines 1. 2. Name: Plot 5 points that have a y value equal to 6 Draw the line y=6 Plot 5 points that have an x value equal to 4 Draw the line x=4 3. 4. Plot 5 points that have an x value equal to -2 Draw the line x=-2 Plot 5 points that have a y value equal to -1 Draw the line y=-1 Unit 1 Constructions and Transformations 1
5. Graph the horizontal and vertical lines given below. a) x 2 b) x 7 c) x 5 d) y 6 e) y 3 6. Reflect the following figure across the line y=1. 7. Reflect the following figure across the line x=2 Unit 1 Constructions and Transformations 2
Part 2: Reflections across horizontal and vertical lines 1. Apply the following transformation to the given figure. Label the vertices of the image. a) x, y 2 x, y A Original A(-4,5) Image C (-3,1) C(-1,3) 2. Apply the following transformations to the given figure. Label the vertices of the image. a) x, y x,4 y Original Image D(1,-1) E(5,-1) F(4,-3) D E G(2,-3) G F Unit 1 Constructions and Transformations 3
3. Time to up our game and do some reflections! a) b) c) d) Unit 1 Constructions and Transformations 4
Geometry Name A m2t0y1u6m NKDubtfaO wswo`fptdwca[reed bltlwci.d F LA]lFlo YrriPgchhtisH krfebseedrlvmejdw. Lesson 9 - More Reflections Graph the image of the figure using the transformation given. Date Period 1) reflection across x = -1 y 2) reflection across x = 2 y x A V x M N W D M H 3) reflection across the x-axis M G y Z 4) reflection across y = -1 y N x x W H Q U r2m0y1^6^ jkvu[tgaq lsyoafqt\wqagrwez vl^lhci. y AQlsly wrqihgchntdsd LroeTsWeSrKvee^dq.Y W MMsa[deX bwnixtghb OIen[fJienTiytuew CGFepoMmpeMtgrZyv. -1- Worksheet by Kuta Software LLC
Write a rule to describe each transformation. 5) J T y 6) y U U' x Q Q' x J' T' T T' A) reflection across x = -3 ) reflection across y = 1 C) reflection across y = 2 D) reflection across x = -1 S A) reflection across y = -1 ) reflection across the y-axis C) reflection across y = -2 D) reflection across x = -2 S' 7) y 8) y U' U V' V J' K' K I' I ' x x J A) reflection across y = -2 ) reflection across x = -2 C) reflection across x = -1 D) reflection across y = -1 A) reflection across y = 3 ) reflection across x = 3 C) reflection across the y-axis D) reflection across x = 1 [ Y2U0r1J6h DKSuCthag xsaobfetfwma`rae` LL[LtC.M L [AXlilO [rxi[gohgtfs_ ZrzetsbeCrsvheMdq.t n XMNardDem qwyidtjh^ KI`nkf[iPnhirtSeo ZGQeGoPmweeturcym. -2- Worksheet by Kuta Software LLC
Geometry Lines of Reflection Name: Mr. Miller (WU 9-27-16) Team: 1. Line segment A has been reflected over line m. Draw line segments AA and. A A' ' m What do you notice about the segments you drew? Explain. 2. Triangle AC has been reflected over line n. Draw segments AA,, and CC. A Fill in the blanks: Line n is the of segments AA,, and CC. C ' n C' A'
3. Draw the line of reflection in each of the figures below. If it is the x or y axis, say so. Otherwise, give an equation for the line. a) b) Line: Line: c) d) Line: Line:
Geometry Reflections Across Diagonals Name: Mr. Miller (WU 9-28-16) 1a) Locate 4 points in the graph that would like on the line y=x. 2a) Locate 4 points in the graph that would like on the line y=-x. b) Draw the line y=x. b) Draw the line y=-x. 2. Reflect triangle RST over the line y=x. S T R
3. Reflect triangle AC over the line y=-x. A C 4. Perform the following transformations.
Lesson 10A Everybody Rotate!!! Name: 1. efore and After a) Use patty paper to rotate the figure 90⁰ counterclockwise. Record the coordinates of the vertices for the original and the transformed figures. ' C Original Rotated A' C' A b) E' F' Original Rotated D' D E F Rule for 90⁰ Counterclockwise Rotations: x, y y, x Unit 1 Constructions and Transformations 1
2. Rotate it 90⁰ Counterclockwise three times! Rotate the given figure 3 times. Record the coordinates of each figure. Label each figure with the proper notations D C A Original Rotated 90⁰ Rotated 180⁰ Rotated 270⁰ Rule for 90⁰ Counterclockwise Rotations: x, y y, x Unit 1 Constructions and Transformations 2
3. One More Time Rotate the figure 3 times. T U S R Original Rotated 90⁰ Rotated 180⁰ Rotated 270⁰ Rule for 90⁰ Counterclockwise Rotations: x, y y, x Unit 1 Constructions and Transformations 3
4. Rotate 90⁰ counterclockwise. Use the rule!!! Record the coordinates of the original figure and its image. a) D C Original Rotated A b) Original Rotated H F S Rule for 90⁰ Counterclockwise Rotations: x, y y, x Unit 1 Constructions and Transformations 4
Geometry The Rule for 90⁰ Rotations Name: Mr. Miller (WU 9-30-16) Team: 1. One last time with tracing paper Rotate 90⁰ counterclockwise. Original Points Image Points Rule for 90⁰ Counterclockwise Rotations: x, y y, x 2. Use the rule!!! Original Points Image Points
Rule for 90⁰ Counterclockwise Rotations: x, y y, x 3. Here s another one. Original Points Image Points 4. Quadrilaterals are people too Original Points Image Points
Lesson 10C Draw the Rotation! Name: 1. Use a protractor and ruler to rotate triangle AC 130⁰ counterclockwise around point P. A C P Unit 1 Constructions and Transformations 1
2. Rotate the figure 60⁰ counterclockwise. 3. Rotate segment A 120⁰ about point P. P C A A P Unit 1 Constructions and Transformations 2
Lesson 10D Angles of Rotation Name: 1. Use a protractor to determine the angle of rotation in the following figures. Unit 1 Constructions and Transformations 1
2. Perform the following rotations. Use the following rules. a) b) c) Unit 1 Constructions and Transformations 2