# 1- Finish the following proof. Given: angle 4 is congruent to angle 5 Prove: m angle 2+ m angle 3 = 90 degrees Statements ...

1- Finish the following proof.

Given: angle 4 is congruent to angle 5

Prove: m angle 2+ m angle 3 = 90 degrees

Statements Reasons

a. ? a. Given

b. a perpendicular to b b. ?

c. ? c. ?

d. m angle 2+ m angle 3 = 90 degrees d. ?

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### 2 Answers

1) `/_4 cong /_5 ` ,diagram as given 1) Given

2) `a _|_ b ` 2) If two lines meet to form congruent adjacent angles, then the lines

are perpendicular.

3) `/_2 ` is complementary to `/_3 ` 3) If the exterior sides of two adjacent angles are perpendicular, then the angles are complementary.

4) `m/_2+m/_3=90 ` 4) Definition of complementary angles

Note that angles 4 and 5 are adjacent as they share a common vertex, a common side, and have no interior points in common. Also, angles 2 and 3 are adjacent for the same reasons. The exterior sides of angles 2 and 3 (the sides that are not shared) are the rays formed by lines a and b.

Given: angle 4 is congruent to angle 5

Prove: m angle 2+ m angle 3 = 90 degrees

Statements Reasons

a. <4 is congruent to <5 a. Given.

b. a perpendicular to b b. <4 and <5 form a linear pair, m<4=m<5=`90^o` ,

a intersects b at right angles.

c. m<4=m<2+m<3=`90^o` c. Vertically opposite angles.

d. m<2+m<3=`90^o` d. Complementary adjacent angles.