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In this lesson, we will learn how to identify congruent triangles using transformations.

Q1:

A triangle π΄ π΅ πΆ has been dilated from a center π by a scale factor of 3 to triangle π΄ π΅ πΆ β² β² β² .

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

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

Q2:

Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.

Q3:

If there exists a combination of rotations, reflections, and translations that would map one shape to another, would the two shapes be congruent?

Q4:

If triangle π΄ is mapped by a reflection in the line π¦ = π₯ to triangle π΄ β² , would the two triangles be congruent?

Q5:

If triangle π΅ is mapped by a 1 8 0 β rotation about the origin to triangle π΅ β² , would the two triangles be congruent?

Q6:

A triangle π΄ π΅ πΆ is rotated by 1 8 0 β about the origin to triangle π΄ π΅ πΆ β² β² β² .

Q7:

The triangle π΄ π΅ πΆ has been transformed onto triangle π΄ π΅ πΆ ο ο ο which has then been transformed onto triangle π΄ π΅ πΆ ο ο ο ο ο ο as seen in the figure.

Describe the single transformation that would map π΄ π΅ πΆ onto π΄ β² π΅ β² πΆ β² .

Describe the single transformation that would map π΄ β² π΅ β² πΆ β² onto π΄ β² β² π΅ β² β² πΆ β² β² .

Hence, are triangles π΄ π΅ πΆ and π΄ β² β² π΅ β² β² πΆ β² β² congruent?

Q8:

Q9:

The figure shows triangles π΄ π΅ πΆ and π· πΈ πΉ .

Are the two triangles congruent?

Justify your answer with one of the following reasons.

Q10:

Q11:

If triangle π is mapped to triangle π β² by a reflection, translation, or rotation, which of the following statements will be true of the two triangles?

Q12:

Triangle π΄ π΅ πΆ has been reflected in the line πΏ to obtain triangle π΄ π΅ πΆ β² β² β² as seen in the given figure.

Are the corresponding angles and sides of the two triangles equal?

What is the length of π΅ πΆ ?

What is the length of π΄ β² π΅ β² ?

What is the perimeter of triangle π΄ π΅ πΆ ?

Q13:

Describe the single transformation that would map π΄ π΅ πΆ onto π΄ π΅ πΆ ο ο ο .

Describe the single transformation that would map π΄ π΅ πΆ ο ο ο onto π΄ π΅ πΆ ο ο ο ο ο ο .

Hence, are triangles π΄ π΅ πΆ and π΄ π΅ πΆ ο ο ο ο ο ο congruent?

Q14:

The figure shows two triangles and .

Work out the size of angle .

What do you notice about the sizes of the angles in both shapes?

Are the two triangles similar?

Q15:

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

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

Q16:

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

Q17:

A triangle π΄ π΅ πΆ has vertices at the points ( β 7 , 4 ) , ( β 4 , 3 ) , and ( β 1 , 3 ) . A triangle π· πΈ πΉ has vertices at the points ( 1 , β 1 ) , ( 4 , β 2 ) , and ( 7 , β 2 ) . By plotting the two triangles and using congruence transformations, decide if the two triangles are congruent.

Q18:

A triangle π΄ π΅ πΆ has vertices at the points ( 0 , 1 ) , ( 1 , 3 ) , and ( β 3 , 3 ) . A triangle π· πΈ πΉ has vertices at the points ( β 2 , β 2 ) , ( β 1 , β 4 ) , and ( β 5 , β 4 ) . By plotting the two triangles and using congruence transformations, decide if the two triangles are congruent.

Q19:

A triangle π΄ π΅ πΆ has vertices at the points ( 0 , 1 ) , ( 1 , 2 ) , and ( 5 , 2 ) . A triangle π· πΈ πΉ has vertices at the points ( 0 , β 1 ) , ( 1 , β 2 ) , and ( 5 , β 1 ) . By plotting the two triangles and using congruence transformations, decide if the two triangles are congruent.

Q20:

Triangle π΄ π΅ πΆ has been rotated to obtain triangle π΄ π΅ πΆ ο ο ο as seen in the given figure.

What is the length of π΄ πΆ ?

What type of triangle is π΄ π΅ πΆ ?

Q21:

In the given figure, β³ π· πΈ πΆ is the image of β³ π΄ π΅ πΆ by reflection in point πΆ . Find the length of π· πΆ , rounding your result to the nearest hundredth.

Q22:

Triangle π΄ π΅ πΆ is right-angled at π΅ with π΄ π΅ = 5 5 c m and π΅ πΆ = 5 2 c m . Let π be the image of π΅ after a translation through 78 cm in the direction of ο« π΅ π΄ . Let π be the image of π΅ under a rotation centre π΄ through angle β 9 0 β . Calculate the length π π to the nearest hundredth.

Q23:

In the given figure, triangle π΄ π΅ πΆ has been reflected to triangle π΄ β² π΅ β² πΆ β² . The perimeter of triangle π΄ π΅ πΆ is 10.5. What is the perimeter of triangle π΄ β² π΅ β² πΆ β² ?

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