The sides PQ- PR of Delta PQR are equal- and S- T are points on PR- PQ such that angle PSQ and angle PTR are right angles- Hence- Delta PTR cong Delta PSQState whether the above statement is true or false-TrueFalse

Question

The sides PQ- PR of Delta PQR are equal- and S- T are points on PR- PQ such that angle PSQ and angle PTR are right angles- Hence-  Delta PTR cong Delta PSQState whether the above statement is true or false-TrueFalse

Toppr Admin · Accepted Answer

Given- PQ-PR and -x2220-PSQ-x2220-PTR-90-x2218-Now- In -x25B3-PSQ and -x25B3-PTRPQ-PR -Given-x2220-PSQ-x2220-PTR -each 90-x2218-x2220-SPQ-x2220-TPR -Common angle-Thus- -x25B3-PSQ-x2245-x25B3-PTR -ASA congruency-

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.

True
False

Given: $P Q = P R$ and $∠ P S Q = ∠ P T R = 90^{\circ}$

Now, In $△ P S Q$ and $△ P T R$

$P Q = P R$ (Given)

$∠ P S Q = ∠ P T R$ (each $90^{\circ}$ )

$∠ S P Q = ∠ T P R$ (Common angle)

Thus, $△ P S Q ≅ △ P T R$ (ASA congruency)

The sides PQ, PR of ΔPQR are equal, and S, T are points on PR, PQ such that ∠PSQ and ∠PTR are right angles. Hence, ΔPTR≅ΔPSQState whether the above statement is true or false.TrueFalse

Given: PQ=PR and ∠PSQ=∠PTR=90∘Now, In △PSQ and △PTRPQ=PR (Given)∠PSQ=∠PTR (each 90∘)∠SPQ=∠TPR (Common angle)Thus, △PSQ≅△PTR (ASA congruency)

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.

True
False

Given: $P Q = P R$ and $∠ P S Q = ∠ P T R = 90^{\circ}$

Now, In $△ P S Q$ and $△ P T R$

$P Q = P R$ (Given)

$∠ P S Q = ∠ P T R$ (each $90^{\circ}$ )

$∠ S P Q = ∠ T P R$ (Common angle)

Thus, $△ P S Q ≅ △ P T R$ (ASA congruency)