Question

Assume you measured <3 and <5 and found them to be equal. Use the spaces provided below to complete a formal proof that demonstrates the picture is level with the trim.

Answer 1

1. S is a straight line that cuts through f and t

2. Given

3. ∠5 ≅ ∠7

4. ∠7 ≅ ∠3 Corresponding angles

Solution:

Step 1: Given

S is a straight line that cuts through f and t

Step 2: Given

∠3 ≅ ∠5

Alternate interior angles are equal.

Step 3: By Vertical angle theorem

Vertically opposite angles are congruent.

∠5 ≅ ∠7

Step 4: Corresponding angles

∠7 and ∠3 are corresponding angles.

∠7 ≅ ∠3

Step 5: Corresponding angles theorem

f || t

Hence proved.