Question

question 9 of 10
the triangles shown below must be congruent.
a. true
b. false

Explanation:

Step1: Calculate the third angle of each triangle

In a triangle, the sum of angles is \(180^{\circ}\). For the first triangle, one angle is \(90^{\circ}\) and another is \(40^{\circ}\). Let the third angle be \(x\). Then \(x + 90^{\circ}+40^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-90^{\circ}-40^{\circ}=50^{\circ}\). For the second triangle, assume the right - angle - like angle is \(90^{\circ}\) (but the marking is not a proper right - angle symbol). If we follow the same sum formula \(y+90^{\circ}+40^{\circ}=180^{\circ}\), \(y = 50^{\circ}\). But the problem is that we don't know if the non - marked angles (the ones that would be \(90^{\circ}\)) are actually equal. Congruent triangles require all corresponding sides and angles to be equal. Just having two angles (\(40^{\circ}\)) and one side (\(12\)) equal is not sufficient as we don't know about the other angles (the supposed right angles). The marking of the first triangle's right angle (\(\square\)) and the second triangle's non - standard marking (\(\checkmark\)) for the 'right - like' angle means we can't confirm angle equality.

Answer:

B. False