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In this lesson, we will learn how to use congruence of polygons to find a missing angle measure or side length.

Q1:

Find π π in the given figure.

Q2:

Q3:

If β³ πΏ π π β β³ π π π , find the values of π₯ and π¦ .

Q4:

Q5:

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

Q6:

Q7:

The perimeter of the polygon π΄ π΅ πΆ π· πΈ is 176 cm and π΄ π΅ πΆ π· πΈ β πΉ π πΏ π· πΈ . Given that πΈ β β ο© ο© ο© ο© β π΄ πΉ and π· πΈ = 4 8 c m , find the perimeter of the figure π΄ π΅ πΆ π· πΏ π πΉ .

Q8:

π΄ π΅ πΆ π· β π πΉ πΈ π· and πΆ is the midpoint of π π· . Given that π πΆ = 3 8 . 1 c m , find the length of π΄ πΈ .

Q9:

Given that the polygons π΄ π΅ πΆ π· and πΈ πΉ πΊ π» are congruent, find the perimeter of the polygon π΄ π΅ πΆ π· and then π β πΉ .

Q10:

If β π΄ is congruent to β π΅ and π β π΄ = 8 1 β , what is π β π΅ ?

Q11:

In the figure, β³ π΄ π· πΈ is congruent to β³ πΆ π΅ πΉ . Given that π β πΉ π΅ πΆ = 2 3 β and π β π· π΄ πΆ = 6 8 β , find π β π· πΈ πΆ .

Q12:

Consider two congruent triangles: β³ π· πΈ πΉ and β³ π π π . Which angle in β³ π π π corresponds to β πΈ ?

Q13:

Given that the dashed line is a line of symmetry of π π π π , which angle has the same size as β π π π ?

Q14:

If the polygon π΄ π΅ πΆ π· π πΏ β the polygon πΎ π π π π πΏ , π΄ π΅ = 8 . 3 cm, and π΅ πΆ = 6 cm, find the perimeter of the polygon π π π π πΎ πΏ .

Q15:

Given that β³ π΄ π΅ πΆ β β³ π π π , find the length of π π and calculate the perimeter of β³ π π π .

Q16:

Find the values of π₯ and π¦ .

Q17:

Q18:

In the following figure, find the length of π π .

Q19:

Given that the two polygons shown are congruent, find the length of πΏ π .

Q20:

Given that the two polygons shown are congruent, find the length of π πΎ .

Q21:

In the figure pentagon is congruent to pentagon .

Work out the length of .

Work out the size of angle .

Q22:

Given that β³ π΄ π΅ πΆ is congruent to β³ π π π , π β π = 3 4 β , and π β π = π β π , find π β π΅ .

Q23:

Consider two congruent polygons π΄ π΅ πΆ π· and π π π πΏ . First, write the line segment in π π π πΏ that corresponds to π· π΄ . Then, find the angle in π π π πΏ whose measure is the same as π β π΅ πΆ π· .

Q24:

What is the condition for two angles to be congruent?

Q25:

In the given figure, π΄ π΅ and π· πΈ are parallel and πΆ lies on both π΅ π· and π΄ πΈ .

Work out the value of π₯ .

Are triangles π΄ π΅ πΆ and πΈ π· πΆ congruent?

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