Question

1. apply casey builds the gate shown, with two solid triangular panels. each support post runs 10 cm above and below the gate. are the solid panels congruent? explain.

Explanation:

• Right - angle triangles: The solid panels are right - angled triangles.
• Angle - Angle - Side (AAS) congruence:
• One pair of corresponding angles: Both triangles have a \(38^{\circ}\) angle.
• Right angles: Both triangles have a \(90^{\circ}\) angle.
• Corresponding sides: The height of each triangle (distance between the support posts, excluding the extra 10 cm above and below which is the same for both) is \(2.5\) m. By the AAS (Angle - Angle - Side) congruence criterion for triangles, if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Answer:

Yes, the solid panels are congruent. Using the AAS (Angle - Angle - Side) congruence criterion, each triangle has a \(90^{\circ}\) angle, a \(38^{\circ}\) angle, and the side opposite the \(38^{\circ}\) angle (the height of the gate, \(2.5\) m) is equal for both triangles. So, the two solid triangular panels are congruent.