Solutions to Unit 4 Review

1. 3x + 2x + 20 + 4x – 20 = 180, so x = 20

measure of angle A = 60, measure of angle B = 60, measure of angle C = 60

triangle ABC is equilateral

2. 55 + 2x + 10 + 2x – 5 = 180, so x = 30

measure of angle A = 55, measure of angle B = 70, measure of angle C = 55

triangle ABC is isosceles

3. Use the distance formula.

AB = square root of 29, BC = square root of 18, AC = square root of 29

Since AB and AC are equal, triangle ABC is isosceles.

4. 120 degrees

5. 30 degrees

6. 30 degrees

7. 120 degreees

8. segments AC and AB are congruent

9. angles F and D are congruent

10. Triangle ABE and Triangle DCE are congruent by SAS

11. The information given is not sufficient to make the triangles congruent. It is SSA.

12. 1. Given

2. Segment BD bisects angle ABC

3. Definition of Equilateral Triangles

4. Definition of Angle Bisector

5. Segment BD = Segment BD

6. Triangle BCD is congruent to Triangle BAD

7. CPCTE/Definition of Congruent Triangles

13. 1. Angle A = Angle 1

2. Given

3. If 2 angles of a triangle are equal, then the sides opposite those angles must also be equal.

4. BD = CD

5. AB = CD; Substitution or Transitive

14. Yes

15. No

16. No

17. Yes

1. equiangular triangle

2. obtuse triangle

3. remote interior angles

4. base

5. scalene

6. flow proof

7. congruence transformation

8. included side

9. coordinate proof

10. vertex angle

11. corollary – a statement that can be easily proved

12. congruent triangles – triangles that have their corresponding parts congruent

13. acute triangle – a triangle in which all the angles are acute angles