Question

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 solid triangular panels
be shown to be congruent by
...
no
yes

Explanation:

Step1: Identify Triangle Parts

Both triangles are right - angled (one angle is \(90^{\circ}\)), have a \(31^{\circ}\) angle, and share the hypotenuse (the vertical side of the gate structure, and also the side between the two triangles). Also, the horizontal sides (2.5 m) are equal.

Step2: Apply Congruence Criterion

We can use the Angle - Angle - Side (AAS) congruence criterion. In AAS, if two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, the triangles are congruent. Here, the right angle (\(90^{\circ}\)), the \(31^{\circ}\) angle, and the side of length 2.5 m (non - included side between the two angles) are equal for both triangles. So the two triangular panels can be shown to be congruent.

Answer:

The solid triangular panels \(\boldsymbol{can}\) be shown to be congruent by \(\boldsymbol{AAS}\) (Angle - Angle - Side) congruence criterion.