Question

Match the picture to the reason that would prove the triangles congruent. (Hint! Look for any additional information given that might not be marked in the picture)

Question 1 options:

4
ASA


5
None


1
AAS


3
HL


6
SSS


2
SAS

1.
congruent triangles

2.
congruent triangles

3.
congruent triangles

4.
congruent triangles

5.
congruent triangles

6.
congruent triangles

Answer 1

SSS

Explanation:

Two triangles are said to be congruent if all their three sides are equal and all of their three angles are equal. There are 5 ways of determining congruent triangle which are:

1. SSS (side, side, side): This is when the two triangles have all three sides equal to each other.
2. SAS (side, angle, side): This is when the two triangles have 2 equal sides and one included angle of both triangles are equal.
3. ASA (angle, side, angle): This is when the two triangles have 2 equal angles and one included side of both triangles are equal.
4. AAS (angle, angle, side): This is when the two triangles have 2 equal angles and one non included side of both triangles are equal.
5. HL (hypotenuse, leg): The hypotenuse is the longest leg of a right angled triangle. If two triangles have equal hypotenuse and one equal leg, they are congruent.

Triangle ABC and triangle BCD are congruent because:

AB = CD, AC = BD and both triangles share the same side BC. That is they have three equal sides (SSS)