Question

The lights shining on a stage appear

to form two congruent right triangles.
Given EC=DB, use Side Angle Side (SAS) to explain why
ECB = DBC.

Answer 1

To prove that ECB is congruent to DBC using SAS, we need to show that they have two pairs of congruent sides and one congruent angle. Given EC = DB and the right angles at C, we can conclude that ECB is congruent to DBC.

Step-by-step explanation:

To prove that ECB is congruent to DBC using SAS, we need to show that they have two pairs of congruent sides and one congruent angle.

Given EC = DB, this gives us one pair of congruent sides.

Next, we know that both triangles share the same hypotenuse CB. Since the hypotenuse is the same and the triangles are right triangles, we can conclude that both triangles have a right angle at C, making the angles ECB and DBC congruent.

Therefore, by using the Side Angle Side (SAS) congruence postulate, we can conclude that ECB is congruent to DBC.