Int. Geometry Unit 2 Test Review 1

Transcription

1 Int. Geometry Unit Test Review irections -: Use the diagram to determine if the angles are vertical, adjacent, supplementary, complementary, or a linear pair. Write all that apply.. and. and and F 9 8. and. 9 and 0 6 E Questions 6-8: Solve for x 6.. x - ( ) 0x - 0 ( ) x ( ) 8. x - ( ) x - ( ) irections 9-: Solve for x and determine if l is perpendicular to m l l 0x - 60 ( ) x + ( ) m x + 6 ( ) x + 6 ( ) m. l x + ( ) ( x - 0) ( x) m

2 Int. Geometry Unit Test Review irections : and are complementary. omplete the following.. m = x; m = x 8. x = m = m = irections : and are supplementary. omplete the following.. m = x 0 ; m = x+. x = m = m =. The supplement of an angle is less than three times the angle. Find the angle, its complement and its supplement. Questions -8: Given OT YS. Use the given drawing and the given information to find the value of x for each case.. If m = x; m = x+ 0 Y V 6. If m = x+ 0 ; m = x+ 0 R O S T. If m = x+ ; m VOS = x 6 Questions If m = y, then find the measure of YOR in terms of y. 9. Two times the supplement of an angle is five times the complement of the angle. Find the measure of the angle.

3 Int. Geometry Unit Test Review Questions 0-9: omplete with sometimes, always, or never. 0. Right angles are vertical angles. ngles,, and are complementary.. Vertical angles have a common supplement.. Perpendicular lines lie in the same plane.. Perpendicular lines form 60 angles.. If a pair of vertical angles are supplementary, then the lines forming the angles are perpendicular. 6. theorem is a true statement.. Supplements of congruent angles are congruent. 8. statement in a proof has a reason. 9. Two angles are supplements. 0. Point E is the midpoint of F. E = x + 0 and F = x 0. Find EF. Questions -0: Write a proof for the statements.. Given: supplements supplements Prove:. Given: complements Prove: O O O

4 Int. Geometry Unit Test Review. Given: complements complements Prove: PS bisects RPT Q R P S T. Given: m m Prove: does not bisect. Given: m m Prove: m m Given: m m Prove: l is not perpendicular to m m l 6 8 k. Given: and are supplementary Prove: 8. Given: FE Prove: EF and are supplements F E

5 Int. Geometry Unit Test Review 9. Given: E and are supplements Prove: E 0. Given: ; and are complementary Prove: Selected nswers:. omplementary, djacent. djacent. Vertical. djacent, Supplementary, Linear Pair. djacent 6. x = 0. x = 8. x = 9. x = ; l m 0. x = ; l is not to m. x = ; l is not to m. x= 8; m = 6 ; m =. x= ; m = ; m =. ngle = 8 ; omp = ; Supp =. x = 6. x = 0 x = 8. ( 80 y). 9. ngle = 0 0. Sometimes. Never. lways. lways. Never. lways 6. lways. lways 8. lways 9. Sometimes 0. EF = 0 Note with the proofs, there are multiple solutions to these problems.... Vertical angles are always congruent.. supplements ;. Given supplements.. Supplements of congruent angles are also congruent and

6 Int. Geometry Unit Test Review 6... complements. Given. m + m = 90. efinition of omplementary ngles. m + m = m O. ngle ddition Postulate. m O = 90. Substitution and. O a right angle. efinition of a Right ngle 6. O O 6. efinition of Perpendicular Lines ( two lines intersect to form a right angle then they must be perpendicular). complements complements,. Given.. ngles complementary to the same angle are congruent.. PS bisects RPT. efinition of an ngle isector (it creates two adjacent congruent angles). Temporarily assume bisects y the definition of an angle bisector. This contradicts the given information that m m, therefore our assumption must be false and does not bisect.. Temporarily assume m = m. Using the ngle ddition Postulate m + m = 80 and m + m = 80. y substitution m + m = m + m We are assuming m = m, so by subtraction m = m. This contradicts the given information m m, therefore our assumption must be false and m m 6. Temporarily assume l m. This means and are both right angles and 90. because they have equal measures. This contradicts the given information m m, therefore our assumption must be false and l is not perpendicular to m

7 Int. Geometry Unit Test Review.. and are supplementary. Given. m + m = 80 o. efinition of Supplementary ngles. m + m = 80 o. ngle ddition Postulate. m + m = m + m. Substitution and. m = m. Reflexive PoE 6. m = m 6. Subtraction PoE and. m = m. Vertical angles are congruent 8. m = m 8. Transitivity PoE (or substitution poe) 6 and 8.. m + m = 80 o. ngle ddition Postulate. m = m FE. Given. m FE+ m = 80 o. Substitution PoE and. FE and are. efinition of supplements. Supplementary ngles 9.. E and are supplements. Given. m E+ m = 80 o. efinition of Supplementary ngles. m E+ m = 80 o. ngle ddition Postulate.. Substitution PoE m E + m = m E + m and. m E = m E. Reflexive PoE 6. m = m 6. Subtraction PoE and

8 Int. Geometry Unit Test Review Given. is a right angle. efinition of Perpendicular Lines. m = 90 o. efinition of a Right ngle. m + m = m. ngle ddition Postulate. m + m = 90 o. Substitution PoE (or transitive) and 6. and are 6. Given complementary. m + m = 90. efinition of complementary angles Substitution PoE m + m = m + m 6 and 9. m = m 9. Reflexive PoE 0. m = m 0. Subtraction PoE 8 and 9