Question Video: Using Properties of Congruence between Two Triangles | Nagwa Question Video: Using Properties of Congruence between Two Triangles | Nagwa

# Question Video: Using Properties of Congruence between Two Triangles Mathematics • First Year of Preparatory School

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Given that β³π΄π΅πΆ β β³πππ, find πβ π΄.

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### Video Transcript

Given that triangle π΄π΅πΆ is congruent to triangle πππ, find the measure of angle π΄.

Since our triangles are congruent, that means their corresponding angles are also congruent which means they are equal in measure. Therefore, angle π΄ is congruent to angle π, angle π΅ is congruent to angle π, and angle πΆ is congruent to angle π.

Now we know that angle π is equal to sixty-six degrees which means angle π΅ is sixty-six degrees. We also know what angles π is equal to, which is equal to thirty-five degrees which means angle πΆ is equal to thirty-five degrees. And we donβt know angle π΄ or angle π. However, we do know that the sum of the measures of the angles on our triangle is equal to one hundred and eighty degrees. Therefore, the measure of angle π΄ plus the measure of angle π΅ plus the measure of Angle πΆ should be equal to one hundred and eighty degrees. Letβs go ahead and plug in sixty-six for angle π΅ and thirty-five for angle πΆ.

Now when weβre solving, we can get rid of the degrees symbol but make sure that we attach it to our answer. So in order to solve for the measure of angle π΄, we need to add sixty-six and thirty-five together. So now we have the measure of angle π΄ plus one hundred and one equals one hundred and eighty. So to solve for the measure of angle π΄, we need to subtract one hundred and one from both sides of the equation. And one hundred and eighty minus one hundred and one is seventy-nine.

Therefore, the measure of angle π΄ is equal to seventy-nine degrees.

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