In isosceles ∆ABC, points M and N belong to base BC
so that BM = CN. Prove:

∆BAM ≅ ∆CAN
∆AMN is an isosceles triangle.

SSS for Side Side Side

Step-by-step explanation:

To prove:

Triangle ABC is isosceles so AB and AC are congruent. BM and NC are congruent because it is given. Since Triangle AMN isosceles the sides AM and AN are congruent. Also the definition of the isosceles Triangle. Because of this the triangles BAM and CAN are congruent.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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