Question

In two triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

Answer 1

Explanation:

Given data:

In two triangles one side an acute angle of one are equal to the corresponding side and angle of the other.

To prove that the triangles are congruent:

Consider two right triangles

$\angle \mathrm{B}=\angle \mathrm{C}=90^{\circ}$ -------- (1)

$A B=D E$ -------- (2)

$\angle C=\angle F$ -------- (3)

Consider ΔABC and ΔDEF,

$\angle C=\angle F$  (using (3))

$\angle B=\angle E$ (using (1))

$A B=D E$ (using (2))

Therefore, ΔABC ≅ ΔDEF by AAS congruence rule.

Hence the triangles are congruent.

To learn more...

1. If two sides and a median bisecting the third side of a triangle are respectively proportional to the corresponding sides and the median of another triangle then prove that the two Triangles are similar.

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2. In two right triangles one side and an acute angle of one are equal to the corresponding side and angle of the other. Prove that the  triangles are congruent.

https://brainly.in/question/681688