Question

1) Which pair of triangles is congruent by Side - Side - Side? *

Answer 1

Answer:

• Pair in diagram 4

Step-by-step explanation:

Diagram 1

One angle marked as congruent, one angle is congruent as vertical angles, one side is marked as congruent:

• ASA

Diagram 2

Two angles and an included side are marked as congruent:

• ASA

Diagram 3

Right angle and one leg marked as congruent, another leg is shared, right angle is included:

• SAS

Diagram 4

Two sides are marked as congruent and one side is shared, so is congruent as well:

• SSS

Answer 2

Answer:

The fourth pair of triangles.

Step-by-step explanation:

Looking at the diagram for the fourth pair of triangles, we see that two pairs of sides have been marked as having the same length, and the remaining side is shared by the two triangles, hence guaranteeing that side's congruence. Therefore, the fourth pair of triangles is congruent by SSS.

The first pair of triangles are congruent by ASA, due to the middle pair of angles being congruent (vert. opp. ∠s), hence providing the condition for SAS.

The second pair of triangles should be SAS, also known as Side - Angle - Side, due to two angles and one side being marked as congruent, and those two angles surrounding the side marked as congruent.

The third pair of triangles should be SAS, due to them sharing a common side and a pair of sides marked congruent, surrounding the right angle. The reason why it is not RHS is because the pair of hypotenuses are not congruent, hence not fulfilling the condition of Right Angle - Hypotenuse (here!) - Side.

Hope this helped!