Question


Congruency of Triangles Practice
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Question
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Triangles upper M upper N upper O and upper P upper Q upper R are graphed side by side on a grid.

ΔOMN≅ΔRPQ
by the HL Theorem. If m∠O=57
degrees, then what is the measure of ∠P
?

(1 point)
degrees

Answers

GPT-4o mini
In congruent triangles, corresponding angles are equal. Since ΔOMN is congruent to ΔRPQ (ΔOMN ≅ ΔRPQ), it follows that m∠O = m∠P.

Given that m∠O = 57 degrees, we can conclude that:

m∠P = 57 degrees.

Therefore, the measure of ∠P is 57 degrees.
that answers is wrong
GPT-4o mini
I apologize for any confusion. Let's analyze the problem again.

If ΔOMN is congruent to ΔRPQ by the HL Theorem (Hypotenuse-Leg Theorem), it means that both triangles are right triangles and share congruent corresponding sides and angles.

Given that \( m∠O = 57^\circ \), we need to determine the measure of \( ∠P \).

In the case of right triangles:

1. Let's assume that \( ∠O \) is one of the non-right angles in triangle OMN.
2. In triangle RPQ, if we denote the right angle as \( ∠Q \) (assuming \( P \) and \( Q \) are the other two vertices), then the corresponding angle \( ∠P \) should be the other non-right angle.

For the angles in a triangle, the sum of the angles in a triangle equals 180 degrees. If we denote the right angle as 90 degrees, then:

\[ m∠M + m∠O + m∠N = 180^\circ \]

Since \( ∠N \) (the right angle) is 90 degrees, we can find the measure of the other angle:

\[ m∠M = 180^\circ - m∠O - 90^\circ = 180^\circ - 57^\circ - 90^\circ = 33^\circ \]

Since the two triangles are congruent, \( m∠M \) in triangle OMN corresponds to \( m∠R \) in triangle RPQ.

Thus, \( m∠P \) and \( m∠R \) together must equal 90 degrees, since \( ∠Q \) is a right angle (as we considered earlier).

If \( m∠R = 33^\circ \), then we follow that:

\[ m∠P = 90^\circ - m∠R = 90^\circ - 33^\circ = 57^\circ \]

But since both angles are actually \( 90^\circ - m∠O \):

So \( m∠P = 90^\circ - m∠O = 90^\circ - 57^\circ = 33^\circ \).

Thus, the measure of \( ∠P \) should be:

\[ m∠P = 33^\circ. \]

Thank you for your patience! So, the corrected answer should be **33 degrees**.

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