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Geometry Chapter 4 Test Review Congruent Triangles Name: Date: Period: 1. Classify βπΈπΉπΊ. F 8 E 9 10 G 2. Name an acute triangle. B 35ο° 55ο° A 30ο° 115ο° 65ο° D 60ο° C 3. How many acute angles can an isosceles triangle have? Explain. 4. Draw and identify a triangle with a) Angle measures of 50ο°, 65ο° and 65ο° b) Angle measures of 80ο°, 75ο° and 45ο° 5. How many obtuse angles can a triangle have? Explain. 6. Find the value of x. 96° x 127° Geometry Chapter 4 Test Review Congruent Triangles Name: Date: Period: 7. Find the value of x. 57° 116° [A] 116 [B] 237 x° [C] 57 [D] 59 8. Find the value of x. οΆοΆο° x 9. Find the measure of the interior angles to the nearest tenth. (Drawing is not to scale.) 3π₯ + 2 ° 4π₯ + 1 ° 2π₯ + 1 ° 10. Find the measure of β‘π΄ below. Geometry Chapter 4 Test Review Congruent Triangles Name: Date: Period: 11. The measure of β‘π΅ is _____. [A] 89° [B] 99° [C] 101° [D] 79° 12. If β π β β‘π and πβ‘π = 2π₯ + 4 and πβ‘π = 34, what is the value of x?. 13. If βπ ππ β βπ½πΎπΏ, then πΏπ½ β _____ . Draw a diagram to support your claim. 14. The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures. d= 33° h e= e 10.1 8.5 f= g= g 57° f 5.5 d h= 15. Sketch the following, if possible. If not possible, state why. A. Right isosceles triangle B. Acute triangle with two obtuse angles C. A triangle with an exterior angle of 45ο° D. A triangle with two acute angles and one obtuse angle 16. In the diagram, β‘π΅ β β‘πΈ and β‘πΆ β β‘πΉ. Find the value of x. B A π₯ + 50 ° 35° C D 75° F E Geometry Chapter 4 Test Review Congruent Triangles Name: Date: Period: 17. Refer to the figure below. Which of the following statements is true? E G D F DEF is equilateral π·πΊ β πΉπΊ [A] βπ·πΊπΈ β βπΉπΊπΈ by SSS [B] βπ·πΌπΊ β βπΉπΌπΊ by SAS [C] βπ·πΉπΊ β βπΊπΈπ· by SSS [D] There are no congruent triangles. 18. State two postulates or theorems that can be used to conclude that βπ΄ππ΅ β βπΆππ·. 19. Refer to the figure shown. Which of the following statements is true? U V W T TV ο WV UV ο XV X [A] βπππ β βπππ by SAS [B] βπππ β βπππ by SAS [C] βπππ β βπππ by ASA [D] βπππ β βπππ by ASA Geometry Chapter 4 Test Review Congruent Triangles Name: Date: Period: 20. Which postulate or theorem can be used to determine the measure of π π? 21. Given:β‘π΅ β β‘πΈ and β‘πΆ β β‘πΉ. What other piece of information is needed to show βπ΄π΅πΆ β βπ·πΈπΉ by ASA Congruence Postulate? [A] β‘π΄ β β‘π· [B] π΅πΆ β πΈπΉ [C] β‘π΅ = β‘πΉ [D] πΈπΉ β πΉπΈ 22. What is the measure of each base angle of an isosceles triangle if its vertex angle measures 40 degrees and its 2 congruent sides measure 23 units? 40° 23 23 23. βπ΄π΅πΆ β βπ·πΈπΉ. Also π΄π΅ β πΈπΉ . What type of triangle is βπ΄π΅πΆ? Explain. 24. In βπ΄π΅πΆ, π΄π΅ β π΅πΆ , which term does NOT describe the triangle? [A] Obtuse [B] Isosceles [C] Equilateral 25. Find the values of x and y. x 112° y [D] Acute Geometry Chapter 4 Test Review Congruent Triangles Name: Date: Period: 26. Use information in the figure below to find πβ‘π·. E 101° D F 27. βπ΄π΅π· β βπΆπ΅π·. Name the theorem or postulate that justifies the congruence. A B D C 28. Given: πΈπ· β₯ πΈπΆ ; π΅π· β₯ π΅πΆ ; πΈπ· β π΅πΆ Based on this information, Prove:βπΆπΈπ· β βπ·π΅πΆ A E B D C 29. Refer to the figure below. A. Is there enough information to know whether β‘πΉπΈπΊ is acute, obtuse, or a right angle? Explain. B. If πβ‘πΉ is less than 45°, what type of angle is β‘πΉπΈπΊ? Explain. 30. Find the measure of β‘π΅. 49° 128° B Geometry Chapter 4 Test Review Congruent Triangles Name: Date: 31. Given: π΅πΆ β π·π΄, β‘1 β β‘2, and πΆπΉ β π΄πΉ Prove: βπΆπΈπΉ β βπ΄πΈπΉ B D 2 1 E C A F 32. Period: Geometry Chapter 4 Test Review Congruent Triangles Name: Date: [1] Scalene [2] οBDC [3] It can have two acute angles if it is a right isosceles or an obtuse isosceles triangle; otherwise it will have 3 acute angles. [4] a. Acute Isosceles 50° 65° 65° b. Acute Scalene 75° 80° 45° [5] One, If you have more than one obtuse angle, the sum of the three angles would be larger than 180. [6] 31° [7] [D] [8] 24° [9] 40.1, 60.7, 79.2 [10] 131° [11] [C] [12] 15 [13] QR [14] d = 5.5, e = 33, f = 90, g = 57, h = 10.1 Period: [15] A, C and D are possible. Sketches vary. B is not possible. [16] 25 [17] [A] [18] SAS and SSS Congruence Postulates [19] [B] [20] AAS [21] [B] [22] 70° [23] Isosceles. οABC ο οDEF , so BC ο EF . Then, since AB ο EF , AB ο BC by the Transitive Property of Congruence. Therefore, οABC is isosceles. [24] [A] [25] π₯ = 44°, π¦ = 68° [26] 39.5° [27] AAS [28] Look below for proof. [29] A. No. There is no information about the measures of angles F and G. B. Obtuse. If οF is less than 45°, οFEH is greater than 45°. Since the 2 triangles are congruent by SAS, οGEH is greater than 45°. Therefore, οFEG is greater than 90°, which means it is obtuse. [30] 79° [28] 1. ED ο EC 2. ο CED is a rt ο 3. BD ο BC 4. ο DBC is a rt ο 1. Given 2. If 2 segm ents areο , they form rt οs. 3. Given 4. If 2 segm ents areο , they form rt οs. 5. ED ο BC 6. DC ο CD 7. ο CED ο ο DBC 5. Given 6. Reflexive 7. HL Congru ence Theorem Geometry Chapter 4 Test Review Congruent Triangles 31. . Statements 1. π΅πΆ β π·π΄ 32. Name: Date: Period: Reasons 1. Given 2. β‘1 β β‘2 2. Given 3. β‘π΅πΈπΆ β β‘π·πΈπ΄ 3. Vertical Angles Theorem 4. βπ΅πΈπΆ β βπ·πΈπ΄ 4. AAS 5. πΈπΆ β πΈπ΄ 5. CPCTC 6. πΆπΉ β π΄πΉ 6. Given 7. πΈπΉ β πΈπΉ 7. Reflexive Property 8. βπΆπΈπΉ β βπ΄πΈπΉ 8. SSS