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In this lesson, we will learn how to identify similar triangles.

Q1:

In the given figure, π΄ π΅ and π· πΈ are parallel. Using the π΄ π΄ criterion, what can we say about triangles π΄ π΅ πΆ and π· πΈ πΆ ?

Q2:

Given that π΄ π΅ and π· πΆ are parallel, are triangles πΈ πΆ π· and πΈ π΄ π΅ similar? If yes, why?

Q3:

The two triangles in the given figure have equal angles. Is this enough to prove that the two triangles are similar?

Q4:

Two triangles are similar. What will be true of the measures of the corresponding angles in the two triangles?

Q5:

Two quadrilaterals have corresponding angles that have equal measures. Can we be sure that the quadrilaterals are similar?

Q6:

Triangles π΄ π΅ πΆ and π΄ β² π΅ β² πΆ β² in the given figure are similar. Work out the value of π₯ .

Q7:

What does the AA criterion for triangles allow us to prove?

Q8:

The figure shows two triangles: and .

Work out the size of angle .

What does the criterion tell us about these two triangles?

Q9:

Q10:

Q11:

The figure shows three triangles: π΄ π΅ πΆ , π΄ β² π΅ β² πΆ β² , and π΄ β² β² π΅ β² β² πΆ β² β² .

Are triangles π΄ π΅ πΆ and π΄ β² β² π΅ β² β² πΆ β² β² similar?

Justify your answer with one of the following reasons.

Q12:

In the given figure, π· πΈ is constructed on the triangle π΄ π΅ πΆ parallel to π΅ πΆ .

What can we conclude about the size of angles π΄ π· πΈ and π΄ π΅ πΆ ?

Using the π΄ π΄ criterion, what can we conclude about triangles π΄ π· πΈ and π΄ π΅ πΆ ?

Q13:

The figure shows two triangles.

Are the two triangles similar?

Why?

Q14:

The figure shows a triangle π΄ π· πΈ where the line segment π΅ πΆ is parallel to π· πΈ

Which angle is equivalent to β π΄ π΅ πΆ ? Give reasons.

Which angle is equivalent to β π΄ πΆ π΅ ? Give reasons.

Hence, are triangles π΄ π΅ πΆ and π΄ π· πΈ similar? If yes, state why?

Q15:

The figure shows two triangles π΄ π΅ πΆ and π· πΆ πΈ where the line segment π΄ π΅ is parallel to π· πΈ

Which angle is equivalent to β π΅ π΄ πΆ ? Give reasons.

Hence, are triangles π΄ π΅ πΆ and πΆ π· πΈ similar? If yes, state why?

Q16:

Triangles π΄ π· πΈ and π΄ π΅ πΆ in the given figure are similar. What, if anything, must be true of the lines β ο© ο© ο© ο© β π· πΈ and β ο© ο© ο© ο© β π΅ πΆ ?

Q17:

Given the following four shapes, which two are similar?

Q18:

Find the size of angle .

The triangles, therefore, share the same angles and are similar. What is the fewest number of angles needed to determine whether two triangles are similar?

Q19:

What is the fewest number of angles needed to determine whether two triangles are similar?

Q20:

Are the two triangles in the figure similar?

Q21:

Are these two triangles similar?

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