$△ A B C$ and $△ P Q R$ may not be congruent, when

A B = P Q

A C = P R

∠ A = ∠ P

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A B = P Q

A C = P R

, Altitude

A D =

Altitude

P S

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A B = P Q

∠ C = ∠ R

∠ B = ∠ Q

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∠ A = ∠ P

∠ B = ∠ Q

∠ C = ∠ R

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Solution

The correct option is C $∠ A = ∠ P$ , $∠ B = ∠ Q$ , $∠ C = ∠ R$
$∠ A = P$ , $B = ∠ Q$ , $∠ C = ∠ S$
This is known as AAA rule which is applicable for similarity of triangles.
Therefore, this conditions do NOT follow rule of congruency.

Hence, option D.

Suggest Corrections

Similar questions

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, then $\frac{A B}{P Q} = \frac{A D}{P M}$

△ A B C

△ P Q R

∠ A = ∠ R, ∠ B = ∠ Q, A B = 28, B C = 10, A C = 24, P Q = 5

Q R = 14

P R

If $Δ A B C \sim Δ P Q R$ and AD and PM are corresponding medians of the two triangles, then

1. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R}, ∠ A = ∠ P$	(a) AA similarity criterion
2. In $Δ A B C$ and $Δ P Q R$ , $∠ A = ∠ P, ∠ B = ∠ Q$	(b) SAS similarity criterion
3. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R} = \frac{B C}{Q R}$ $∠ A = ∠ P$	(c) SSS similarity criterion
4. In $Δ A C B, D E \| \| B C$ $\Rightarrow \frac{A D}{B D} = \frac{A E}{C E}$	(d) BPT

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