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ASA Criteria for Congruency of Triangles

Question 147 ...

Question

Question 147

If $Δ P Q R$ and $Δ S Q R$ are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are $Δ P S Q$ and $Δ P S R$ congruent? Which condition do you use?

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Solution

In $Δ P S Q$ and $Δ P S R$ , PQ = PR [given]
SQ = SR [given]
PS = PS [common side]

By SSS congruence criterion, $Δ P S Q ≅ Δ P S R$

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Q. Triangles ABC and PQR are both isosceles with AB = AC and PQ = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use? If ∠B =50°, what is the measure of ∠R?

Q. Question 5
S and T are point on sides PR and QR of

Δ P Q R

∠ P = ∠ R T S

Δ R P Q \sim Δ R T S

Δ P Q R

is an isosceles triangle such that PQ=PR , then prove that the attitude PS from P on QR bisects QR

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ASA Criteria for Congruency of Triangles

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