Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry Chapter 4 Review. 1. Classify as equilateral, isosceles, or
Document related concepts
Transcript
Geometry Chapter 4 Review. 1. Classify OPQ as equilateral, isosceles, or scalene. P 8 O 10 9 Q 2. Name a right triangle. B 35° 55° A 30° 115° D 65° 60° C [A] ABC [B] ADB [C] BDC [D] none of these 3. Complete the statement using one of the following words: always, sometimes, or never. “An isosceles triangle is ______ an obtuse triangle.” 4. How many acute angles can an isosceles triangle have? Explain. 5. A scalene triangle can have how many right angles? Explain your reasoning. 6. Find the value of x: 84° 128° x [A] 128° [B] 84° [C] 32° [D] 148° 7. Find the measure of the interior angles to the nearest tenth. (Drawing is not to scale.) ( x 1) (3x 1) ( x 1) [A] 36.2 , 40.9 , 102.9 [B] 39.3 , 34.8 , 105.9 [C] 35.3 , 37.8 , 106.9 [D] 36.8 , 36.8 , 106.4 8. Use the figure below to solve for x. ( x 10) 2x 55 [A] 145 [B] 45 [C] 90 [D] 55 9. Refer to the figure below. mA ______. [A] 67 [B] 74 [C] 35 [D] 141 10. Which figures appear to be congruent? 1 2 4 3 5 [A] 3 and 4 [B] 1 and 3 [C] 1, 3, and 4 [D] 4 and 5 11. Which two figures shown below appear to be congruent? A. B. C. D. 12. Consider a triangle, DEF . Must it be true that DEF FED ? Explain. 13. In the diagram, B E and C F . Find the value of x. B A bx 50g D 75 [B] x 75 [C] x 35 [D] x 50 C F E [A] x 25 35 14. If ABC GHJ and DEF GHJ , then ABC DEF . What property of congruence does this statement represent? 15. Refer to the figure below. Give a congruence statement for two triangles in the figure. E G D F DEF is equilateral. DG ~ = FG 16. Refer to the figure shown. Give a congruence statement for the two triangles and name the theorem or postulate that proves the congruence. I K H J HI JK L IJ LK 17. You are making a patch for a quilt. You cut the pieces so that XR YZ and XY RZ . Show that XRZ ZYX and state the congruence postulates you use. X Y R P Z Q 18. Which postulate or theorem can be used to determine the measure of RT ? [A] SSS Congruence Postulate [B] AAS Congruence Theorem [C] ASA Congruence Postulate [D] SAS Congruence Postulate 19. Given: AB DE B E Prove: ABC DEC 20. Phillip walked 80 yards to the southwest while Shondra walked 140 yards to the west. Meanwhile, 220 yards to the southeast, José walked 140 yards to the northeast and LuYin walked 80 yards to the east. The angle formed between the walking paths of Phillip and Shondra is congruent to the angle formed by the walking paths of José and LuYin. If Phillip and Shondra are now 101 yards apart, how far apart are José and LuYin? How do you know? 21. Given: BC DA, 1 2, and CF AF Prove: CEF AEF B D 2 1 E C A F 23. What can you conclude about EGF? A G C E F B 24. In ABC , if AB BC and mA 39 , then mC ______. [A] mB [B] 39 [C] 141 [D] 102 25. Given: ED EC; BD BC; ED BC Prove: CED DBC A E B D C 26. ABD CBD . Name the theorem or postulate that justifies the congruence. A B D C [A] SAS [B] ASA [C] AAS [D] HL 27. Place a square in a convenient position in the first quadrant of a coordinate plane. Label each vertex using variables for each of the coordinates. Be sure to use the fewest possible variables. 28. Use the labeled diagram and a coordinate proof to prove that in an equilateral triangle the triangle formed by connecting the midpoints of each side is F IJ equilateral. AH a, a 3K G X b g B 0, 0 Y Z b g C 2a , 0 Reference: [4.1.1.1] [1] scalene Reference: [4.1.1.4] [2] [A] Reference: [4.1.1.7] [3] Sometimes Reference: [4.1.1.10] [4] It can have two acute angles if it is a right isosceles or an obtuse isosceles triangle; otherwise it will have 3 acute angles. Reference: [4.1.2.13] [5] 1; a scalene triangle cannot have 2 or 3 right angles because the sum of the measures of the angles in a triangle is 180 . Reference: [4.1.2.15] [6] [D] Reference: [4.1.2.19] [7] [D] Reference: [4.1.2.25] [8] [B] Reference: [4.1.2.27] [9] [A] Reference: [4.2.1.30] [10] [B] Reference: [4.2.1.32] [11] B and D Reference: [4.2.1.38] [12] No. In order for DEF FED , DEF must be isosceles or equilateral. Reference: [4.2.2.45] [13] [A] Reference: [4.2.2.47] [14] Transitive Property Reference: [4.3.1.50] [15] DGE FGE Reference: [4.3.1.59] [16] HIJ JKL by the SAS Congruence Postulate Reference: [4.3.2.61] Statements 1. XR YZ [17] Reasons Given XY RZ 2. XZ XZ Reflexive property of congruence 3. XRZ XYZ SSS congruence postulate Reference: [4.4.1.64] [18] [B] Reference: [4.4.1.66] Statements Reasons 1. AB DE 1. Given [19] 2. B E 2. Given 3. ACB DCE 3. Vertical s Thm. 4. ABC DEC 4. AAS Congruence Thm. Reference: [4.4.2.71] [20] 101 yards; SAS Congruence Post. Reference: [4.5.1.74] [21] BEC DEA by vertical angles. BEC DEA by AAS. Then, because corresponding parts of congruent triangles are congruent, CE AE . EF EF by the Reflexive Property. So CEF AEF by SSS. Reference: [4.5.2.75] [22] Students’ proofs should explain how all three segments of the construction are copied and are therefore congruent to the segments in the original angle. They should then use the SSS Congruence Postulate to show that the two triangles are congruent. Next, they should use congruent parts of congruent triangles to prove that the corresponding angles are congruent. Reference: [4.6.1.79] [23] EGF is equilateral and equiangular. Reference: [4.6.1.82] [24] [B] Reference: [4.6.2.87] 1. ED EC 2. CED is a rt 3. BD BC [25] 4. DBC is a rt 5. ED BC 6. DC CD 7. CED DBC Reference: [4.6.2.86] [26] [D] Reference: [4.7.1.91] 1. Given 2. If 2 segments are , they form rt s. 3. Given 4. If 2 segments are , they form rt s. 5. Given 6. Reflexive 7. HL Congruence Theorem [27] b g ba, ag b0, 0g ba, 0gx y 0, a Reference: [4.7.2.96] [28] First, calculate the midpoint of each side: X = Fa , a 3 I, Z = ba, 0g, and Y = F3a , G G H2 2 J K H2 I J K a 3 . Second, using the Distance Formula, find 2 the length of each segment connecting those midpoints: F a 3 I F aI G G J K a, H 2 K H2 J 2 distance of XZ = Fa 3 I F aI G G J K a, H2 K H2 J 2 2 distance of YZ = 2 and the distance of XY = 02 a 2 a. Since each of the sides are the same length, the inscribed triangle is equilateral.
