Draw two triangle ABC and XYZ and show AAS congruency...
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Answer:
a triangle, the sum of three angles is 180°.
Therefore, in PQR, ∠PRQ + ∠PQR + ∠QPR = 180°.
Therefore, 70° + 50° + ∠QPR = 180°
⟹ ∠QPR = 180° – (70° + 50°)
⟹ ∠QPR = 180° – 120°
⟹ ∠QPR = 60°.
In ∆PQR and ∆XYZ,
PQ = XZ, ∠PRQ = ∠XYZ = 70° and ∠QPR = ∠YXZ = 60°.
Therefore, by AAS (Angle-Angle-Side) criterion, the two triangles are congruent.
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Step-by-step explanation:
In the above figure, Δ ABC and Δ PQR are congruent triangles. This means,
Vertices: A and P, B and Q, and C and R are the same.
Sides: AB=PQ, QR= BC and AC=PR;
Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.
Congruent triangles are triangles having corresponding sides and angles to be equal. Congruence is denoted by the symbol “≅”. They have the same area and the same perimeter.
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