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In this lesson, we will learn how to identify congruence in triangles using different criteria and use this to find unknown angles or sides.

Q1:

Are two triangles congruent if both triangles have the same side lengths?

Q2:

In the given figure, . Determine .

Q3:

In the following figure, find .

Q4:

Given that , , and , determine .

Q5:

Determine the value of π₯ in the given congruent triangles.

Q6:

In the following figure, find π β π π π .

Q7:

Given that β³ π π π β β³ π π π , find the values of π₯ and π¦ .

Q8:

In the figure, π΅ π· meets π΄ πΈ at πΆ , which is also the midpoint of π΅ π· . Find the length of πΆ πΈ .

Q9:

Given that β³ π΄ π΅ πΆ β β³ π π π , and π β π΄ + π β π΅ = 1 1 7 β , what is π β π ?

Q10:

Given that π΄ π΅ πΆ π· is a square, find π β π πΆ π΅ .

Q11:

From the information in the figure, what is π β π΅ π πΆ ?

Q12:

In the figure below, π· π π πΈ is a rectangle. Find π β π΄ πΈ π· .

Q13:

Triangles π΄ π΅ πΆ and πΈ π· πΉ are congruent. What is the perimeter of β³ π΄ π΅ πΆ ?

Q14:

Consider the figure, then complete the following using < , = , or > : π π π π .

Q15:

Given that π΅ πΆ = π΄ π· , π΄ πΆ = π΄ πΈ , and π β πΆ π΄ π΅ = 6 8 β , find π β πΈ π΄ π· .

Q16:

Given that β³ π΄ πΈ πΆ and β³ π΅ πΉ π· are congruent, what is the measure of β π΅ π· πΉ ?

Q17:

Given that triangle π΄ π΅ πΆ is congruent to triangle π π π , find π β π΅ .

Q18:

Find π β π΅ π΄ πΈ .

Q19:

The two triangles in the given figure are congruent. Work out the area of triangle π΄ π΅ πΆ .

Q20:

If β³ π΄ π΅ πΆ β β³ π΄ π΅ π· , the perimeter of π΄ πΆ π΅ π· = 3 9 4 c m , and π΄ π΅ = 5 6 c m , find the perimeter of β³ π΄ π΅ πΆ .

Q21:

Given that β³ π΄ π΅ πΆ β β³ π΄ π΅ π· , find the perimeter of π΄ πΆ π΅ π· .

Q22:

Given that β³ π΄ π΅ πΆ is congruent to β³ π π π , first find the length in β³ π π π that is equal to π΄ π΅ . Then find the angle in β³ π΄ π΅ πΆ with the same measure as β π .

Q23:

In the figure, and are congruent.

Work out the length of .

Work out the size of angle .

Q24:

In the figure shown, π β π΅ π· πΈ = 5 0 β . What is π β πΈ π΄ πΆ ?

Q25:

Suppose β³ π΄ π΅ πΆ β β³ π π π . If the perimeter of β³ π΄ π΅ πΆ is 14, π π = 3 , and π π = 5 , what is π΄ πΆ ?

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