Geometry Review. Description. Question #1. Question #2. Question #3. ΔDEC by ASA? 5/17/2017 Synergy TeacherVUE. Geometry CSA Review

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1 escription Geometry S Review Geometry Review Question #1 If Δ and ΔXYZ are congruent, which of the following statements below is not true? ngle and angle Y are congruent. ngle and angle ZXY are congruent. and XY are congruent. and XZ are congruent. Question #2 Given that X, and E XW, what is the third congruence needed to prove that ΔXWY ΔE by S? Y Y E W W E Question #3 GEO 4.0 ngles Use the figure to answer the following question(s). 1/16

2 Given P Q and T is a transversal, which of the following justifies 1 5? orresponding ngles Postulate lternate Interior ngles Theorem onsecutive Interior ngles Theorem lternate Exterior ngles Theorem Question #4 Use the figure below to answer the following question: Given that and bisect each other at E, which of the following justifies ΔE ΔE? SSS Postulate SS Postulate efinition of Segment isector efinition of ongruent Triangles Question #5 2/16

3 Given: Line segment WZ bisects line segment XY Line segment XY bisects line segment WZ To prove: Triangles WX and ZY are congruent Statement: 1. Segment WZ bisects XY 2. Segments X and Y are congruent Reasons: 1. given 3. Segment XY bisects WZ 3. given 4. ngles WX and YZ are congruent 5. Triangles WX and ZY are congruent 2. when a segment is bisected the resulting segments are congruent 4. Opposite interior angles of intersecting lines are equal 5. Triangles with two sides and an included angle equal are congruent What should be in statement 4 to complete the proof? Step 4 is not needed the proof works without it. Segments W and Z are congruent. Segments WX and YZ are congruent. ngles WX and ZY are congruent. Question #6 3/16

4 Triangle is reflected over the line y = x to produce triangle '''. What will be the coordinates of '? (2, 1) ( 2, 1) (2, 1) (1, 2) Question #7 In the diagram below, and E are parallel. Which of the following statements must be true? is a right angle and E are congruent Triangles and E are similar. None of the above Question #8 Look at on the coordinate plane. 4/16

5 Which coordinate plane shows after a 90 degree clockwise rotation about the origin? 5/16

6 Question #9 Which theorem or postulate can be used to prove Δ Δ? Given: and S SSS S Question #10 efine perpendicular lines. Lines that cut across two or more lines. Two coplanar lines that do not intersect. Two coplanar lines that intersect at a 90 degree angle. Two non coplanar lines that do not intersect. 6/16

7 Question #11 In order to show that ΔFGH is congruent to ΔF'G'H', how many degrees must ΔFGH be rotated clockwise about the origin? Question #12 Examine Δ below. etermine which of the following relationships are true. Select all that apply. E = 2 m = 2(m E) E Question #13 7/16

8 Identify the triangles below that are similar by SS similarity. Question #14 ased on the drawing below, in order for Δ to be similar to ΔEF by SS similarity, which of the following needs to be true? m = 38 m = 52 m F = 38 m F = 52 Question #15 8/16

9 Hank writes a proof to show that vertical angles are congruent. Given: Lines m and n intersect at a point. Prove: 1 2 STTEMENTS 1. Lines m and n intersect at a point Given RESONS 2. 1 and 3 are linear pairs 2 and 3 are linear pairs 3. 1 and 3 are supplementary angles 2 and 3 are supplementary angles efinition of linear pairs Linear pairs are supplementary 4. efinition of supplementary angles 5. Substitution property 6. m 1 = m 2 Subtraction property efinition of congruent angles Part Which is the missing statement in step 4? Part Which is the missing statement in step 5? Question #16 9/16

10 Mark is asked to prove that 4 6, given that, as shown in the diagram above. Mark's proof is shown in the table below. Step in Proof Statements therefore m 4 = m therefore m 8 = m 6 3 If m 4 = m 8 and m 8 = m 6 then m 4 = m Which reason supports the statement Mark made in step 2 of his work? Vertical angles are congruent. Supplementary angles are congruent. orresponding angles formed by parallel lines are congruent. lternate interior angles formed by parallel lines are congruent. Question #17 alculate the length of the side given the following data for 58 : Sin 58 = os 58 =.530 Tan 58 = Question # /16

11 Find the value of x. 16sin(35 ) 16cos(35 ) sin(35 ) sin(35 ) Question #19 Use the figure below to answer the following question. If E, which of the following justifies Δ ~ ΔE? efinition of Similar Triangles SS Similarity Theorem SSS Similarity Theorem Similarity Postulate Question # /16

12 Marcus made a sail for his toy boat. If the sail is 5 inches long and the top angle of the sail is 40, what is the width of the bottom of the sail (w) to the nearest tens place? 3.2 inches 3.9 inches 4.2 inches 5.0 inches Question #21 What is the approximate value of x in the figure below? Question # /16

13 Question #22 Right triangle QRS is pictured below. Which equation gives the correct value for RS? cos 31 = 24.8 RS cos 31 = RS 24.8 sin 31 = 24.8 RS sin 31 = RS 24.8 Question #23 The sun is behind a building and casting a shadow. pproximately how long is the shadow if the building is 25 feet tall and the angle of the shadow opposite the building is 27? (ssume the building is at a right angle to the ground.) sin cos tan ft ft ft..02 ft. Question # /16

14 Find the volume of a sphere with a diameter of 22m. Round to the nearest tenth. 44,579.6 m3 5,572.4 m3 1,393.1 m m3 Question #25 Find the volume of the cylinder. Round the answer to the nearest hundredth ft ft ft ft3 Question # /16

15 This figure shows a pyramid with an altitude of 10 cm and an equilateral triangle base with sides 12 cm long. What is the volume of this equilateral pyramid? Question #27 sphere has a radius r = 3 inches. What is its approximate volume? V = 4 3 πr3 8π in3 12π in3 36π in3 108π in3 Question # /16

16 Find the volume of the cone and round to the nearest tenth in in in in /16