A proof of the Alternate Interior Angles Theorem, using parallel lines a and b with transversal m, is shown below. Given: alb
m is the transversal.
Prove: 23 25
12
43
5 6
8 7
Proof:
Statements
Reasons
1. Lines a and bare parallel with 1. Given
transversalm
2. 21 - 25
2. Corresponding Angles Postulate
3.23* 21
3. Vertical Angles Theorem
4.23 - 25
Which property is used in step 4?
reflexive property
transitive property
associative property
commutative property

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality