1. Chapter 5 Properties of Triangles Problems Chapter 5 Properties of Triangles Problems

2. Page 221 # 1-4, all In Exercises 1-4 CD is the perpendicular bisector of AB Properties of Triangles 5.1 AD = ½ (AB) Equal False C A B D

3. Page 221 # 5-8, all In Exercises 5-8 OM is the angle bisector of < LOM Properties of Triangles 5.1 Congruent ML ML = MN Prove ∆ LMO = ∆ LMO by AAS then CPCTC L N O M True

4. Page 223 # 31 -34 In Exercises 31 - 34, Use C (1, 1), D ( 7, 4 ), E (3, 6). At which point does the bisector intersect CD? Find an equation of the perpendicular bisector? ● ● D (7, 4) E (3, 6) C (1, 1 ) ● 5.1 ● (4, 5/2) y = ─2 x + 21/2 ( y 2 – y 1 )= (4 – 1)= 3= 1 (x 2 – x 1 )= (7 – 1)= 6= 2 y = – 2 x + ? 5/2 = – 2 (4) + ? 5/2 = – 8 + ? 5/2 + 8 = ? 5/2 + 16/2 = 21/2 Properties of Triangles ( 7 + 1) 2 (4 + 1) 2 =45252

5. Page 223 # 32 -34 In Exercises 32 Does the perpendicular bisector of CD pass through E? ● E (3, 6) ● 5.1 ● (NO) 3,6 is not ony = ─2 x + 21/2 ( y 2 – y 1 )= (4 – 1)= 3= 1 (x 2 – x 1 )= (7 – 1)= 6= 2 y = – 2 x + ? 5/2 = – 2 (4) + ? 5/2 = – 8 + ? 5/2 + 8 = ? 5/2 + 16/2 = 21/2 y = – 2 x + 21/2 6 = – 2 (3) + 10.5 6 = – 6 + 10.5 6 = 4.5 ? No, E is not on graph Properties of Triangles

6. Page 223 # 35-40 In exercises 35 – 40, match angle or segment with it’s measure W T S U X V 50⁰ 40⁰ ─ y 3 x + 1 x + 3 2 4 y 35)SU 36)< VWX 37)< WVX 38)WT 39)< XTV 40)< XVT 4 40⁰ 50⁰ 6 60⁰ 30⁰ Properties of Triangles

7. Given: In exercises 1 – 6. is OB a perpendicular bisector, an angle bisector, an angle bisector, a median or an altitude of ∆ MPB 1)Given:MO OP 2)Given:OB MP 3)Given:< MBO < PBO 4)Given:OB MP and MO OP 5)Given:∆ MOB ∆ POB 6)Given:BO bisects < MPB 5.1 Properties of Triangles Median Altitude < bisector bisector bisector,< bisector, median, altitude < bisector Page 227 # 1-10, all In exercises 7-10, complete the statement using always, sometimes, never 7) A median ____________ has a midpoint as an endpoint 8) An altitude ________________ lies outside a triangle 9) A perpendicular bisector _________________ has a vertex as an endpoint 10) The angle bisectors of a triangle ______________ intersect at a single point always sometimes always B P O M

8. Given: In exercises 11 – 14. decide whether the statement is true or false 11)A perpendicular bisector can also be an attitude 12)An incenter can also be a circumcenter 13)An angle bisector cannot be a median 14)The circumcenter is the center of the inscribed circle of a triangle 5.1 Properties of Triangles Page 227 # 11-14 9 B FHD True False I G O 4 9 7.5 8 1/21/3 48

9. Page 229 # 30-32 In Exercises 30-32, Use the graph to describe the relationships among the lines. Then use the coordinates to find the slope of each line and verify your results. A (0, 0) B (12, 6) C (18, 0) 30)Find equations of the lines that contain the three medians of ∆ ABC 31)Find equations of the lines that contain the three altitudes of ∆ ABC 32)Find equations of the lines that contain the three perpendicular bisectors of ∆ ABC Properties of Triangles A (6, 3) ● ● ● ● A (9, 0)

10. Page 229 # 30-32 In Exercises 30-32, Use the graph to describe the relationships among the lines. Then use the coordinates to find the slope of each line and verify your results. A (0, 0) B (12, 6) C (18, 0) 30)Find equations of the lines that contain the three medians of ∆ ABC 31)Find equations of the lines that contain the three altitudes of ∆ ABC 32)Find equations of the lines that contain the three perpendicular bisectors of ∆ ABC Properties of Triangles A (6, 3) ● ● ● ●

11. Page 229 # 33 In Exercise 33, Given l is parallel to n, what is the value of x ? Properties of Triangles 130° 30° x > > l n 50°30° 100° x = 80°

12. Page 229 # 34 In Exercise 34, what is the value of a + b ? Properties of Triangles 140° 40° > > a + b = 140° ba

13. Page 236 # 4- 8 1) A midsegment of a triangle is a segment that connects he midpoints of two sides of the triangle. 2) A triangle has 3 midsegments. 3) Midsegment Theorem is the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length. Properties of Triangles D A C B E Median Altitude Angle Bisector Perpendicular Bisector Midsegment D A E C B

14. Page 236 # 9-16 In exercises 9 – 16, In ∆ ABC, the midpoints of the sides are L, M and N Properties of Triangles N M L C B A 9LM ǁ 10AB ǁ 11If AC = 14, then LM = 12If MN = 8, then AB = 13IF NC= 3, then LM = 14IF LN = 5, then _____ = 10 15IF LM = 3 x – 1 and BC = 10 x – 6, Then LM = 16If NM = x – 1 and AB = 3 x – 7, then AB = BC MN 7 16 3 AC 7 8