Casey builds the gate shown to the right, with two solid triangular panels. Each support post runs 10 cm above and below the gate. Are the solid panels congruent? Explain

The two solid triangular panels are congruent by the AAS Congruence Theorem.

When two angles and a non-included side of a triangle are congruent to two angles and a non-included side of another, the triangles are congruent by the AAS Congruence Theorem.

In the image given, we have the following:

Therefore, the two solid triangular panels are congruent by the AAS Congruence Theorem.

Learn ore about the AAS Congruence Theorem on:

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Congruent

Step-by-step explanation:

There are two triangular panels ΔABC and ΔDBE used in the gate.

Since, ∠ABC ≅ ∠DBE [Given]

∠ACB ≅ ∠DBE [Given]

AB ≅ DE [Given]

Therefore, by AAS postulate of congruence, both the triangles will be congruent.

ΔABC ≅ ΔDBE

Hence, we can say that the solid panels used in the gate are congruent.

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