Math 120 Review Questions Chapters 2 and 3
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1 Math 120 Review Questions hapters 2 and 3 1. State whether the stateents are always true (), soeties true (S), or never true (N). a. Two parallel lines are coplanar. b. The easure of an exterior angle of a triangle is greater than the easure of any interior angle. c. Two isosceles triangles with congruent bases are congruent. d. ll diagonals of a regular pentagon are congruent. e. If the nuber of sides of a polygon is doubled, then the su of the exterior angles is doubled. f. If two lines are cut by a transversal, then the alternate interior angles are congruent. g. When there is a transversal of two lines, the three lines are coplanar. h. n equilateral triangle is a right triangle. i. Two lines that have no point in coon are parallel. j. If the easure of one angle of a triangle is greater than the easure of a second angle, then the side opposite the larger angle is longer than the side opposite the saller angle. 2. oplete the following table for a regular polygon. Nuber of sides Nuber of diagonals Measure of each interior angle Measure of each exterior angle Given: (8x) 58 (5x 8.5) l Find x. re l and parallel? Why or why not? 4. Find x, y, and z. a. Given : l b. Given: Δ with 75 z l x 125 y x y 32 z
2 5. onstruct using copass and straight edge: a. The three edians of a scalene triangle. b. The three altitudes of an isosceles triangle. c. The three perpendicular bisectors of a right triangle. 6. Prove by using the indirect ethod of proving. T a. Given: TI RG, TR TG Prove: TI does not bisect RTG (This proves that an altitude of a scalene triangle is not an angle bisector.) R I G b. The perpendicular bisector of a line segent is unique. O 7. Given: 1 is copleentary to 2 2 is copleentary to 3 Prove: RV PE R 1 2 V P 3 E 8. Given: E is altitude to is altitude to E Prove: E E 9. Given:, Prove: Δ E is isosceles E 10. Provide a drawing, given, prove and two-colun proof for the given stateent: The edian to the base of an isosceles triangle is the altitude to the base of the triangle.
3 11. Given the following letters: N M E Z Y O U T H a. Which letters have syetry with respect to a line? b. Which letters have syetry with respect to a point? 12. a. Which geoetric figures have syetry with respect to a line? b. Which geoetric figures have syetry with respect to a point? 13. oplete the figure so that it reflects across line. 14. Which type of transforation (slide, reflection, rotation) is illustrated? a. b. c.
4 nswer Key: 1. a. b. S c. S d. e. N f. S g. h. N i. S j. 2. opleted Table: No. of sides Nuber of diagonals Measure of each interior angle Measure of each exterior angle (6) (20) (144 ) (72 ) 3. x = 7.25 ; l and are not parallel because the corresponding angles are not. 4. a. x = 75, y = 55, z = 50 b. x = 58, y = 58, z = onstructions will be discussed in class. 6. a. Proof by indirect ethod: 1) Suppose TI does bisect RTG 2) Then RTI GTI... efinition of angle bisector TI RG... Given RIT GIT... efinition of lines. TI TI... Identity ΔRIT Δ GIT... S TR TG... PT This contradicts the given that TR is not to TG. 3) Supposition ust be false. Therefore, TI does not bisect RTG. M
5 b. Given: M, M idpoint of Prove: M is the only bisector of Proof by indirect ethod: 1) Suppose that M is another bisector of. 2) M, M idpoint of... Given M... efinition of bisector M and M are right s... lines for right s M = 90, M= ef of right s M+ M= M... ngle ddition Postulate 90 + M= Substitution M= 0... Subtraction Property This contradicts the Protractor Postulate. 3) Supposition is false. Therefore M is the only bisector of 7. Proof: STTEMENTS RESONS 1. 1 copleentary to 2, 1. Given 2 copleentary to Two s copleentary to the sae angle are congruent. 3. RV PE 3. ITLT so that corresponding s are, then the lines are parallel. 8. Proof: STTEMENTS RESONS 1. E is altitude to, is 1. Given altitude to E, 2. E, E 2. efinition of altitudes 3. and E are right s 3. lines for right angles 4. E 4. ll right angles are congruent Identity 6. Δ Δ E 6. S 7. E 7. PT 9. Proof: STTEMENTS RESONS 1., 1. Given Identity 3. Δ Δ 3. SS PT 5. E E 5. If 2 s of a Δ are, then the sides opposite the s are 6. Δ E is isosceles 6. efinition of isosceles triangle
6 10. Given:, idpoint of Prove: Proof: STTEMENTS RESONS 1., idpoint of 1. Given efinition of idpoint Identity 4. Δ Δ 4. SSS PT efinition of perpendicular lines. 11. a. M E Y O U T H b. N Z O H 12. a. pentagon, cross, star b. parallelogra, cross 13. opleted drawing 14. a. reflection b. slide c. rotation
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