Question

solve it as soon as possible​

Answer 1

Solution :

$\longrightarrow$ The triangles are similar they may be congruent.

$\longrightarrow$ Triangles BAP and CAQ are isosceles triangles since

$\longrightarrow$ AP = AB in triangle BAP, an isosceles triangle has two equal sides

and sides AC = AQ in triangle CAQ, an isosceles triangle has two equal sides

• < APB = < ABP in triangle BAP, this is a property of isosceles triangles

• < ACQ = < AQC in the triangle CAQ, this is a property of isosceles triangles

$\longrightarrow$ Since < BAP in triangle BAP = < CAQ in triangle CAQ

• < APB + <ABP + < BAP =180, property of triangles

and < ACQ + < AQC + <CAQ = 180, property of triangles

then

• < APB + <ABP = < ACQ + < AQC

further since < APB = < ABP and < ACQ = < AQC

• 2 < APB = 2< ACQ, by substitution

Then

• < APB = < ABP = < ACQ = <AQC

Triangles BAP and CAQ are similar by angle, angle, angle

To prove them congruent sides AB (= AP)in triangle BAP would have to equal AC (= AQ) in triangle CAQ or side BP ( in BAP) would have to equal CQ ( in CAQ)

I hope it helps you ❤️✔️