Question

Given: M is midpoint of AB, ME ⊥ AC, MF ⊥ CB, ME ≅ MF

Prove: ∡CAB ≅ ∡CBA

Answer 1

Prove : Angle CAB is congruent to Angle CBA

Step-by-step explanation:

Given: ME ⊥ AC, MF ⊥ CB, ME ≅ MF and M is the midpoint.

Since MF ⊥ CB, Angle MFB = 90 degree.

Since ME ⊥ AC, Angle MEA = 90 degree.

ME congruent to MF (given)

Since, It is given that Point M is a midpoint, MA is congruent to MB

This proves that Triangle MEA is congruent to Triangle MFB by SideAngleSide property.

Therefore, Angle CAB is congruent to Angle CBA through CPCTC property.

(Corresponding Parts of Congruent Triangles are Congruent.)

Hope it helps :D