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Honors Geometry Chapter 5 Review Sheet Name: _____________________________________ 1. In ΔXYZ, ZX XY YZ a) List the angles in order from least to greatest. b) XZ = 3x – 6 and ZY = x + 8 c) What are the restrictions on x? A 2. Given: AD is the median to BC. AD 3 x 2 BD 5 x 3 DC 2 x 6 Find the length of AD. B D C 3. Write a compound inequality for the possible measures of L. 4. List the angles of ∆GHI in order from smallest to largest measure. 5. List the sides of ∆PQR in order from shortest to longest. For numbers 6 & 7, fill in the blank to complete each sentence. 6. A(n) __________________ is a segment that joins a vertex of a triangle and is perpendicular to the side opposite to the vertex. 7. The ____________________ of a triangle is equidistant from the vertices of the triangle. 8. Write an inequality relating m∠1 to m∠2. 9. Write an inequality relating AB to DE. 10. Write an inequality about the length of GH . 11. Complete the proof by supplying the missing information for each corresponding location. Given: AB = DE, and BE > AD Prove: mCAE > mCEA Statements 1. AB = DE Reasons 1. Given 2. BE > AD 2. Given 3. AB DE 3. Def. of segments 4. __________________________ 4. Reflexive Prop. 5. mCAE > mCEA 5. ____________________________________ 12. The vertices of ∆XYZ are X(0, 4), Y(6, 12), and Z(12, 2). Find the coordinates of the centroid of ∆XYZ. 13. Write a valid inequality of the restrictions on x. (5x – 10)° 14. The perpendicular bisectors of ∆ABC meet at point G. Find GC. AD = 24, BG = 25, GH = 7. (2x)° A 2 D 2 B C G R 7 H 15. The angle bisectors of ∆ABC meet at point G. Find GD. A 12 AD = 12, BG = 15, GH = 9. D C G R 1 9 H B 16. P is the circumcenter of ∆XYZ. Find PZ. SX = 3, SP = 4, RZ = 12. X 3 S R 4 12 P Y Z 17. P is the incenter of ∆XYZ and ZP = 15, XN = 24, and XP = 26. Find PO. X M 26 24 P Y N 15 O Z Use the following information for numbers 18 – 22: L is the centroid of ∆MNO, NP = 14, ML = 20, and NL = 9. 18. PO = ? . M 19. MP = ? . R 20. NQ = ? . 21. LQ = ? . 22. Perimeter of ∆NLP 20 Q L 9 N ? . 14 P O