Question

ij ⊥ hi and fg ⊥ ef. complete the proof that ∠efg ≅ ∠hij.

statement	reason
2. fg ⊥ ef	given
3. m∠hij = 90°	definition of perpendicular lines
4. m∠efg = 90°
5. m∠hij = m∠efg	transitive property of equality
6. ∠efg ≅ ∠hij	definition of congruence

Explanation:

Step1: Recall perpendicular lines definition

Perpendicular lines form right angles (90°). For step 4, since \( \overleftrightarrow{FG} \perp \overleftrightarrow{EF} \), by the definition of perpendicular lines, the measure of \( \angle EFG \) is 90°.

Step2: Identify the reason for step 4

The reason for \( m\angle EFG = 90^\circ \) is the same as step 3, which is the definition of perpendicular lines (because \( \overleftrightarrow{FG} \perp \overleftrightarrow{EF} \) implies the angle between them is 90°).

Answer:

Definition of perpendicular lines