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The sides \( P Q , P R \) of a triangle \( P Q R \) are equal. and \( S , T \) are points on \( P R , P Q \) such that \( \angle P S Q \) and \( \angle P T R \) are right angles. Prove that the triangles \( P T R \) and \( P S Q \) are congruent if \( Q S \) and \( R T \) intersect at \( X \) . Prove that the triangle \( P T X \) and \( P S X \) are congruent.

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Similar Questions

Q1

The sides PQ, PR of triangle PQR are equal, and S,T are points on PR,PQ such that

∠ P S Q a n d ∠ P T R

are right angles.
And hence, the triangles PSR and PSQ are congruent
If the above statement is true then mention answer as 1, else mention 0 if false

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Q2

The sides PQ, PR of $Δ P Q R$ are equal, and S, T are points on PR, PQ such that $∠ P S Q$ and $∠ P T R$ are right angles. Hence, $Δ P T R ≅ Δ P S Q$

State whether the above statement is true or false.

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Q3

PQR is an isosceles triangle whose equal sides PQ and PR are at right angles. S and T are points on PQ such that

Q S = 6 S P

and

Q T = 2 T P . P R S = θ, P R T = ϕ

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Q4

In fig(iv), T is a point on side QR of triangle PQR and S is a point such that RT = ST. Prove that PQ + PR > QS

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Q5

S

and

T

are points on sides

P R

and

Q R

of

△ P Q R

such that

∠ P = ∠ R T S

. Show that

△ R P Q \sim △ R T S

.

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