Question

prove that the angle opposite to the equal side of equilateral traingle are equal.

Answer 1

Answer:

Angles opposite to equal sides of a triangle are equal. Sides opposite to equal angles of a triangle are equal. Each angle of an equilateral triangle is of 60°. If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence .

Answer 2

Answer:

Given:Isosceles triangle ABCABC

i.e., AB=ACAB=AC

To prove:\angle{B}=\angle{C}∠B=∠C

Construction:Draw a bisector of \angle{A}∠A intersecting BCBC at DD.

Proof:In \triangle{BAD}△BAD and \triangle{CAD}△CAD

AB=ACAB=AC(given)

\angle{BAD}=\angle{CAD}∠BAD=∠CAD by construction

AD=ADAD=AD(common)

\therefore \triangle{BAD}\cong\triangle{CAD}∴△BAD≅△CAD by SAS congruence rule.

Thus, \angle{ABD}=\angle{ACD}∠ABD=∠ACD by CPCT

\Rightarrow \angle{B}=\angle{C}⇒∠B=∠C

Hence, angles opposite to equal sides are equal.

Hence proved.

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