Ready to Go On? Skills Intervention 1-1 Understanding Points, Lines, and Planes

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1 1 Read to Go On? Skills Intervention 1-1 Understanding Points, Lines, and Planes Find these vocabular words in Lesson 1-1 and the Multilingual Glossar. Vocabular point line plane collinear coplanar segment endpoint ra opposite ras Naming Points, Lines, and Planes. Name collinear points. δ Z T r Points that lie on the same line are Name three points on line r. Name the points on line s. X Q M s. Name lines. To name a line, use either, or two. Name line s using two points on the line. Name the line containing point Z. Identifing Points and Lines in a Plane In what plane does Z lie? What other points lie in this plane? Drawing Segments and Ras Draw and label each of the following.. segment with endpoints H and Z Draw two dots and label them H and Z Use a straightedge to connect the points.. ra TR Draw two dots and label them T and R. eginning at T, connect the points and etend through R. Draw an arrow to indicate that the ra etends forever. Holt Geometr

2 1 Read to Go On? Skills Intervention 1- Measuring and Constructing Segments Find these vocabular words in Lesson 1- and the Multilingual Glossar. Vocabular coordinate distance length congruent segments construction between midpoint bisect Finding the length of a segment Find each length.. MP What are the coordinates of M? and P? MP Substitute the coordinates of M and P. Subtract. Take the absolute value of the difference.. NQ What are the coordinates of N? and Q? NQ Substitute the coordinates of N and Q. Subtract. M N P Q Take the absolute value of the difference. Using the Segment ddition Postulate. L is between K and M. KL = 43 and KM = Find LM. Since L is between K and M, KL. Substitute the known lengths into the equation: LM Solve the equation to find LM.. is between and C. Find. 100 C Since is between and C, C C Substitute these values into the equation. Simplif the right side of the equation. Get the variable on one side of the equation. Simplif. Substitute the value of to find Simplif. 11( ) Using Midpoints to Find Lengths Point M is the midpoint of X. XM 5 3, and M 9 5. Find, XM, M, and X. Since M is the midpoint of X, what do ou know about XM and M? Write an equation b substituting epressions for XM and M. Solve the equation to find the value of. XM 5 3 ; M 9 5 ; X 3 Holt Geometr

3 1 Read to Go On? Skills Intervention 1-3 Measuring and Constructing ngles Find these vocabular words in Lesson 1-3 and the Multilingual Glossar. Vocabular angle measure acute angle right angle obtuse angle congruent angles angle bisector Naming ngles Name angles in the diagram. ou can name an angle in three was: b its verte, b a on each ra and the, or b a. How man angles are in the diagram? Point P is called the of all of the angles. Name three angles. Q P 1 R S Measuring and Classifing ngles Find the measures of each angle. Then classif each angle as acute, right, or obtuse.. OC The measure of an angle is the of the of the real numbers that the ras correspond with on a protractor. moc. If an angle measures greater than 90 and less than 180, the angle is. So, OC is a(n) angle O C. O The real number that O corresponds with is. The real number that O corresponds with is. mo ;. If an angle measures greater than 0 and less than 90, the angle is. So, O is a(n) angle. Finding the Measure of an ngle TX bisects MTR, mmtx (9 7), and mxtr (6 8). Find mxtr. Since TX bisects MTR, mmtx. Substitute the given values and write an equation. Solve for. To find mxtr, substitute for. mxtr 6 8 6( ) 8 4 Holt Geometr

4 1 Read to Go On? Skills Intervention 1-4 Pairs of ngles Find these vocabular words in Lesson 1-4 and the Multilingual Glossar. Vocabular adjacent angles linear pair complementar angles supplementar angles Identifing ngle Pairs Tell whether the angles are onl adjacent, adjacent and form a linear pair, or not adjacent.. 3 and Do 3 and 4 have a common verte? Do 3 and 4 have a common side? Do 3 and 4 have common interior points? and 4 are.. 7 and 8 Do 7 and 8 have a common verte? Do 7 and 8 have a common side? Do 7 and 8 have common interior points? 7 and 8 are. C. 5 and 6 Do 5 and 6 have a common verte? Do 5 and 6 have a common side? Do 5 and 6 have common interior points? 5 and 6 are. Finding the Measures of Complements and Supplements If mr (14 3), find each of the following.. complement of R To find the measure of the complement of an angle, the measure of the angle from. Find the measure of the complement of R b subtracting (14 3) from. (14 3) ( ). supplement of R To find the measure of the supplement of an angle, the measure of the angle from. Find the measure of the supplement of R b subtracting (14 3) from. (14 3) 5 Holt Geometr

5 1 Read to Go On? Quiz 1-1 Understanding Points, Lines, and Planes Draw and label each of the following. 1. a line containing points R and S. a ra with endpoint that passes through L 3. a plane containing a segment with endpoints X and 4. three coplanar lines intersecting in three points. Name each of the following. 5. three collinear points 6. a plane containing X,, and δ R X m 7. two segments 8. a line containing and T T 1- Measuring and Constructing Segments Find the length of each segment. 9. _ D 10. _ 11. _ C C D Sketch, draw, and construct a segment congruent to PQ _. P Q 6 Holt Geometr

6 1 Read to Go On? Quiz continued 13. T is between R and V. RV 31 and VT 14. Find RT. 14. N is between M and P. Find MN. _ M is the midpoint of. M 11 9, and M M N P Find. 16. Find M. 17. Find M. 1-3 Measuring and Constructing ngles 18. Name all the angles in the diagram. R T 1 S V Classif each angle b its measure. 19. mxz mpqr mrz 178. MT bisects LMP, mlmt (4 13), and mtmp ( 17). Find mlmp. 3. Use a protractor and a straightedge to draw a 70 angle. Then bisect the angle. 1-4 Pairs of ngles Tell whether the angles are onl adjacent, adjacent and form a linear pair, or not adjacent. 4. and and and 1 If mp (9 0), find the measure of each of the following. 7. supplement of P 8. complement of P 7 Holt Geometr

7 1 Read to Go On? Enrichment Measuring ngles and Segments For Eercises 1 1, use the figure at the right and the information provided to find each angle measure. mxtz 54 mrtq 1 TP bisects QTZ X Z T S P R Q 1. mxts. mstr 3. mqtz 4. mqtp 5. mptz 6. mtz 7. mxt 8. mrtp 9. mptx 10. mrtx 11. mxtq 1. mstq The figure at right is a number line without tic marks. For Eercises 13 18, use the number line _ and the information provided. _ D is the midpoint of CH. G is the midpoint of DH. F is the midpoint of DG. C D F G H Find the coordinates D 14. G 15. F _ Find the lengths. 16. DF 17. CG 18. GH 19. DG 0. DH 1. CH 8 Holt Geometr

8 1 Read To Go On? Skills Intervention 1-5 Using Formulas in Geometr Find these vocabular words in Lesson 1-5 and the Multilingual Glossar. Vocabular perimeter area base height diameter radius circumference (pi) Finding Perimeter and rea Find the perimeter and area. 14. What is the formula for perimeter of a rectangle? Substitute the known values into the formula Simplif. What is the formula for the area of a rectangle? Substitute the known values into the formula. Simplif.. What is the formula for perimeter of a triangle? Substitute the known values into the formula. Simplif. 1 m m 16 m What is the formula for the area of a triangle? 3 m Substitute the known values into the formula. Simplif. Finding the Circumference and rea of a Circle Find the circumference and area of a circle with radius 1 cm. Use the ke on our calculator and round to the nearest tenth. 1 cm What is the formula for the circumference of a circle? Substitute the known values into the formula. Simplif. What is the formula for the area of a circle? Substitute the known values into the formula and simplif. 9 Holt Geometr

9 1 Read To Go On? Skills Intervention 1-6 Midpoint and Distance in the Coordinate Plane Find these vocabular words in Lesson 1 6 and the Multilingual Glossar. Vocabular coordinate plane leg hpotenuse Finding the Coordinates of a Midpoint Find the coordinates of the midpoint of KL with endpoints K(9, 4) and L(7, 6). Write the Midpoint Formula. Substitute the coordinates of K and L into the midpoint formula. _ Simplif to find the coordinates of the midpoint. _ Finding the Coordinates of an Endpoint M is the midpoint of PR. P has coordinates (7, 1), and M has coordinates (1, 4). Find the coordinates of R. The coordinates of R are unknown. Let the coordinates of R equal (, ). 7 ppl the Midpoint Formula. (1, 4), 1 Write and solve an equation to find the -coordinate of R. 7 1 Write and solve an equation to find the -coordinate of R. 1 + The coordinates of R are (, ). Finding Distances in the Coordinate Plane Use the Distance Formula and the Pthagorean Theorem to find the distance, to the nearest tenth, from K to L. Write the Distance Formula. What are the coordinates of K? of L? Substitute the coordinates of K and L into the Distance Formula. 3 K 4 O L M Simplif. The length of _ KL is. Write the Pthagorean Theorem. Substitute the lengths of the legs into the Pthagorean Theorem to find the length of the hpotenuse. Simplif. The length of the hpotenuse KL is. 10 Holt Geometr

10 1 Read To Go On? Skills Intervention 1-7 Transformations in the Coordinate Plane Class Find these vocabular words in Lesson 1-7 and the Multilingual Glossar. Vocabular transformation preimage image reflection rotation translation Identifing Transformations Identif the transformation. Then use arrow notation to describe the transformation.. Is each point and its image the same distance from C a line of reflection? Is each point and its image the same distance from a point P? Have all of the points in the figure moved the same distance in the same direction? ased on the information above, identif the transformation. Use arrow notation to describe the transformation. C. Is each point and its image the same distance from a line of reflection? Is each point and its image the same distance from a point P? Have all of the points in the figure moved the same distance in the same direction? ased on the information above, identif the transformation. D C D C Use arrow notation to describe the transformation. Drawing and Identifing Transformations figure has vertices at X (5, 4), (, 0) and Z (5, 4). fter a transformation, the image has vertices at X (5, 4), (, 0) and Z (5, 4). Draw the preimage and image. Then identif the transformation. Plot the points and label each verte. Connect the vertices. How is each point related to its image? Identif the transformation. 4 4 O 4 X 4 Translations in the Coordinate Plane 4 K Find the coordinates for the image of JKL after the translation L (, ) ( 4, 3). Draw the image. J What are the coordinates of J, K, and L? J(, 0), K(3, ), L(, ) O L 4 To appl (, ) ( 4, 3), subtract from the -coordinate of each verte and subtract from the -coordinate of each verte. Find the coordinates of J, K, and L. J(3, ), K(, 0), L(, ) K Plot the image points. Connect the vertices. 11 Holt Geometr

11 1 Read to Go On? Quiz 1-5 Using Formulas in Geometr Find the perimeter and area of each figure cm cm 7 15 cm 5. Find the circumference and area of a circle with radius 11 in. Use the ke on our calculator and round to the nearest tenth. 1-6 Midpoint and Distance in the Coordinate Plane 6. Find the coordinates of the midpoint of _ HJ with endpoints H(7, 4), and J(3, ). 7. S is the midpoint of _ RT, R has coordinates (5, 1) and S has coordinates (1, 4). Find the coordinates of T. 8. Using the distance formula, find LM and NP to the nearest tenth. Then determine if _ LM _ NP. M 6 4 O N L P 1 Holt Geometr

12 1 Read to Go On? Quiz continued 9. Using the Distance Formula and the Pthagorean Theorem, find the distance, to the nearest tenth, from X(3, ) to (3, 1). 1-7 Transformations in the Coordinate Plane Identif the transformation. Then use arrow notation to describe the transformation D C C D D C D C O 1. Find the coordinates for the image of figure JKLM after the translation (, ) (, ). Graph the image. K 6 J K 4 L 4 O M M 13. figure has vertices at P(6, ), Q(3, 3) and R(1, ). fter a transformation, the image of the figure has vertices at P(0, ), Q(3, 7) and R(5, ). Graph the preimage and image. Then, identif the transformation. P 6 4 P 4 O 4 R R 13 Holt Geometr

13 1 Read to Go On? Enrichment Reflections Use the figure at the right to answer each question. 1. Reflect WX over the -ais. Label the vertices of the image W, X, and respectivel.. Find the coordinates of W, X, and. 3. How are the coordinates of the preimage related to the coordinates of the image? 4 W O W 4 X 4 6 Use the Distance Formula to find each of the following to the nearest tenth. 4. WX 5. X 6. W 7. W X 8. X 9. W 10. How are the lengths of the segments of the preimage related to the lengths of the segments in the image? 11. Find the perimeters of each triangle. 1. How are the perimeters related? 13. What are the lengths of the base and height of WX? 14. What is the area of WX? 15. What are the lengths of the base and height of W X? 16. What is the area of W X? 17. How are the areas related? 18. What do ou think is true about the perimeter and area of the image of WX after a translation? Wh? 14 Holt Geometr

1-1 Understanding Points, Lines, and Planes (pp. 6 11) Vocabulary EXERCISES

1-1 Understanding Points, Lines, and Planes (pp. 6 11) Vocabulary EXERCISES Vocabulary acute angle.................. 1 adjacent angles.............. 8 angle....................... 0 angle bisector............... 3 area........................ 36 base........................ 36