Question

Show that the perpendiculars drawn from the vertices of the base of an isosceles triangle to the opposite sides are equal.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

AE = BD (Proved)

Step-by-step explanation:

See the diagram attached.

Δ ABC is an isosceles triangle and ∠ CAB = ∠ ABC ........ (1)

Now, BD ⊥ AC and AE ⊥ BC.

Take triangles Δ ABE and Δ BAD,

(i) ∠ BEA = ∠ ADB = 90° {Given}

(ii) ∠ DAB = ∠ EBA {From equation (1)}

(iii) AB is the common side.

Hence, by Angle-Angle-Side i.e. AAS criteria we can say that Δ ABE ≅ Δ BAD.

Therefore, AE = BD (Proved)

{Those are corresponding sides of the two congruent triangles}