If two shapes are congruent, are they also similar? Explain your answer.
If two shapes are similar, are they also congruent? Explain your answer.
If shape A is similar to shape B and shape B is similar to shape C. Are shapes A and C similar?
Are all squares similar? Explain your answer.
The smaller quadrilateral has been reflected, then enlarged and then rotated to create the larger quadrilateral.
Are the two shapes similar?
Which side in the larger shape is corresponding to side AB?
Which angle in the larger shape is corresponding to \angle ADC?
In the diagram, a smaller rectangle is inscribed within a larger rectangle.
Are the two rectangles similar?
If the length of FG remains fixed, what must be the length of BG so that the two rectangles are similar?
Consider the two similar triangles:
State the angle that corresponds to:
Which side does DB correspond to in \triangle PQR?
Which side does BC correspond to in \triangle PQR?
Consider the two similar triangles:
Which side does DE correspond to in \triangle LMN?
Which side does DC correspond to in \triangle LMN?
Consider the following shapes:
Are the shapes similar?
Find the enlargement factor.
Determine the reduction factor for the two circles shown:
For each pair of similar shapes below:
Find the enlargement factor.
Find the value of the pronumeral.
Pythagorean triples such as 3, 4, 5 represent lengths of possible right-angled triangles. Consider a triangle with side lengths 15 \text{ cm}, 20 \text{ cm} and 25 \text{ cm}.
Find the enlargement factor that needs to be applied to a triangle with side lengths measuring 3 \text{ cm}, 4 \text{ cm} and 5 \text{ cm}, to get a triangle with side lengths measuring 15, 20 and 25 \text{ cm}.
Verify that a triangle with side lengths measuring 15 \text{ cm}, 20 \text{ cm} and 25 \text{ cm} satisfies Pythagoras’ theorem.
Dave wants to transform a shape but wishes it to remain similar to the original shape. Is he able to maintain similarity for each of the following transformations?
Rotation
Reflection
Translation
Enlargement
Consider the two shapes below:
Are the two shapes similar?
State if the following statements are true or false:
One of the shapes is a rotation of the other.
One of the shapes is a translation of the other.
One of the shapes is an enlargement of the other.
For each pair of shapes, state whether the two shapes are similar and give a reason for your answer:
In congruent triangles, what is the ratio of corresponding sides?
For each of the following sets of triangles, state the two triangles that are similar and state the similarity test they satisfy:
Triangle 1
Triangle 3
Triangle 2
Triangle 1
Triangle 3
Triangle 2
Triangle 4
Triangle 1
Triangle 3
Triangle 2
Triangle 4
Triangle 1
Triangle 3
Triangle 2
Triangle 4
Triangle 1
Triangle 3
Triangle 2
Triangle 4
Consider the triangles shown below:
Which pair of triangles are similar?
Which similar triangles test can be used to show that these two triangles are similar?
Given that all three angles in one triangle match all three angles in another triangle, are these triangles definitely similar? Explain your answer.
For each pair of triangles, find the value of x, giving reasons:
The following two triangles are similar:
Comparing the side lengths of the two triangles, state the ratio of corresponding sides.
Find the value of:
s
n
m
In the diagram, JK \parallel MN such that \triangle LJK and \triangle LNM are similar:
Write down the angle that is equal to:
Identify the side in \triangle LMN that corresponds to:
In the diagram, JK \parallel MN:
Write down the angle that is equal to \angle LJK. Give a reason as to why they are equal.
Write down the angle that is equal to \angle LKJ. Give a reason as to why they are equal.
Use the correct mathematical notation to state that the two triangles are similar.
In the diagram below, \triangle JIK \sim \triangle LIM:
Write down the angle that is equal to \angle IKJ. Give a reason for your answer.
Write down the angle that is equal to \angle IJK. Give a reason for your answer.
Complete the statement: \dfrac{IJ}{IL} = \dfrac{JK}{⬚}.
Consider the diagram below:
State the reason that \triangle ABC similar to \triangle AED.
Use the correct mathematical notation to state that the two triangles are similar.
Consider the pair of triangles shown below:
Which rule can be used to show that the two triangles are similar: AAA, SSS, SAS or RHS?
Calculate the value of the unknown side length x.
Which of these triangles are similar? Give a reason for your choice.
Which of these triangles are similar? Give the reason for their similarity.
Which of these triangles are similar? Give the reason for their similarity.
Consider the diagram shown:
Why is BE parallel to CD?
Which angle is equal to \angle BEA?
How do we know that
\triangle ABE \sim \triangle ACD?
State the enlargement factor going from the smaller triangle to the larger triangle.
Find the value of the pronumeral.
The pair of triangles in the diagram already have one pair of angles identified as being equal.
Determine the minimal condition needed to identify if these are similar triangles.
The triangles in the diagram have angles as marked.
Determine the minimal condition needed to identify if these are similar triangles.
The pair of triangles in the diagram have side lengths as labelled.
Determine the minimal condition needed to identify if these are similar triangles.
Determine whether the following statements, together with the information on the diagram, form a set of minimal conditions that can be used to prove if the triangles are similar:
One more corresponding side length (not opposite the given angle).
Another pair of corresponding angles.
Two corresponding side lengths.
Two more pairs of corresponding angles.
Determine, with full reasoning, whether or not the pair of triangles shown below are similar:
Prove that these two triangles are similar:
Determine whether triangles \triangle ABC and \triangle DFE are similar, giving reasons:
Prove that \triangle ABC and \triangle EGF are similar:
Consider \triangle ABC and \triangle PQR:
Prove that \triangle ABC is similar to \triangle PQR.
Find the value of x.
Find the value of y.
Consider the triangles \triangle LMN and \triangle LKJ:
If JK \parallel MN, prove that \triangle LMN and \triangle LKJ are similar.
Consider the diagram below:
Prove that \triangle AOB and \triangle DOC are similar.
Hence, show that AB \parallel CD.
In the diagram, QR \parallel ST:
Show that \triangle PQR is similar to \triangle PST.
Find the scale factor of enlargement.
Find the value of f.
In the diagram, \triangle ABC is a right-angled triangle with the right angle at C. The midpoint of AB is M and MP is perpendicular to AC.
Prove that \triangle AMP is similar to \triangle ABC.
Find the ratio of AP to AC.
In the diagram, AB = 7, BC = 10.5 and BE = 6.
Prove that the \triangle ABE and \triangle ACD are similar.
Find the value of f.
Consider the diagram below:
Prove that \triangle ABE is similar to \triangle BCD.
Prove that \triangle EDB is similar to \triangle BCD.
Can we conclude that \triangle ABE is similar to \triangle EDB?
