a Similar triangles have the same shape. What does this mean for the triangle's angles?
B
b Congruent triangles have the same size. What does this mean for the triangle's sides?
A
a Yes, they are similar.
Explanation: See solution. Flowchart: See solution.
B
b Yes, they are congruent.
Explanation: See solution.
Practice makes perfect
aSimilar triangles have the same shape. For this to be true, they must have three pairs of congruent corresponding angles. However, as long as at least two pairs are congruent, the third pair must be as well. This is called the Angle-Angle Similarity. Examining the diagram, we can identify two pairs of congruent angles.
∠ A ≅ ∠ D ⇒ m∠ A = m∠ D
∠ B ≅ ∠ E ⇒ m∠ B = m∠ E
Therefore, we can use Angle-Angle Similarity to claim similarity. Let's show this as a flowchart.
b If the triangle's are congruent, they are identical. In addition to having the same shape, they must also have the same size making corresponding sides congruent. Let's take a look at the labeled sides.
In both triangles, the side that is labeled is between the 74^(∘) angle and the unknown angle. Therefore, theses sides must be corresponding. Since these corresponding sides and the corresponding angles are congruent, the triangles are also congruent.
