# Identify Congruent Triangles

In this worksheet, students will identify congruent triangles and give reasons for their congruence.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Apply Facts About Angles and Sides

Difficulty level:

### QUESTION 1 of 10

Triangles which are exactly the same shape and size are congruent.

Note: this also applies to shapes other than triangles.

Triangles are congruent for the following reasons:

Three matching sides (SSS)

Two matching sides and the angle between them (SAS)

Two matching angles and a corresponding side (AAS)

In a right-angled triangle, the hypotenuse and one matching side (RHS)

Now it's over to you. You will identify congruent triangles and give reasons as to why they are in fact, congruent.

Look at the two triangles below and select the option which best describes the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which best describes the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at two triangles below and identify the reason which best describes their relation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which best describes their relation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

Not congruent

Congruent (SSS)

Congruent (SAS)

Congruent (AAS)

Congruent (RHS)

• Question 1

Look at the two triangles below and select the option which best describes the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Congruent (SSS)
EDDIE SAYS
The two triangles have three, equally matching sides therefore they are congruent. Strong start.
• Question 2

Look at these two triangles and select the option which best describes the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Not congruent
EDDIE SAYS
In order for the two triangles to be congruent they would need another matching side. Did you spot that?
• Question 3

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Not congruent
EDDIE SAYS
Again, between the two triangles there's not enough information. If we knew that the two unmarked sides were equal to one another than we would know the two triangles are congruent to one another.
• Question 4

Look at two triangles below and identify the reason which best describes their relation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
EDDIE SAYS
Did you notice that? The SAS rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. Then the two triangles are congruent.
• Question 5

Look at these two triangles and select the option which best describes their relation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Congruent (RHS)
EDDIE SAYS
The hypotenuse (the two longest sides) and matching sides of the right-angled triangles are equal. Therefore the two triangles are congruent. Don't panic if you struggled, you can always look back to the introduction to jog your memory.
• Question 6

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Not congruent
EDDIE SAYS
The triangles are similar but not congruent as the lengths of each side could be different.
• Question 7

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Congruent (SAS)
EDDIE SAYS
In this instance the two triangles are congruent as two sides and the angle between them match!
• Question 8

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Not congruent
EDDIE SAYS
We are unable to say that the two triangles are congruent as the sides do not necessarily match between them both. Take a deep breath, you've got this!
• Question 9

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Congruent (AAS)
EDDIE SAYS
These two triangles are congruent as two angles and a matching side are equal to one another.
• Question 10

Look at these two triangles and select the option which matches the situation.

If the triangles are congruent, select the option with the reason for them being congruent.

CORRECT ANSWER
Congruent (SAS)
EDDIE SAYS
The triangles are congruent as there are two sides and an angle in between them which are equal. Great work! That's another activity ticked off.
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