Write the following using mathematical symbols: triangle ABC is similar to triangle DEF.
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 pair of hexagons:
Are the two shapes similar?
Determine which of the following statements is true:
One shape is a rotation of the other.
One shape is a translation of the other.
One shape 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:
State the enlargement factor for the following pair of triangles:
If shape A is similar to shape B, and shape B is similar to shape C, are shapes A and C similar?
If two shapes are congruent, are they also similar? Explain your answer.
If two shapes are similar, are they are also congruent? Explain your answer.
Determine whether the following statements are true or false:
All circles are similar.
All rectangles are similar.
All squares are similar.
All equilateral triangles are similar.
If every angle in an n sided polygon matches exactly with an angle in another n sided polygon, does this mean that the two polygons are definitely similar? Explain your answer.
Given that all three angles in one triangle match all three angles in another triangle, can you be sure these triangles are similar?
State the ratio of corresponding sides for two congruent triangles.
A square has a side length measuring 4 units and a rhombus has a side length measuring 8 units.
Are the sides of the two shapes in the same ratio?
Explain why the two shapes may not be similar.
The smaller quadrilateral has been reflected, then enlarged and finally rotated to form the larger quadrilateral:
Are the two shapes congruent, similar, or neither?
Which side in the larger shape is corresponding to side AB?
Which angle in the larger shape is corresponding to \angle ADC?
Consider the two similar triangles:
Identify the angle corresponding to the following:
\angle D
\angle B
\angle C
CD corresponds to which side in \triangle RPQ?
CB corresponds to which side in \triangle RPQ?
Consider the two similar triangles:
Identify the angle corresponding to the following:
\angle D
\angle B
\angle C
DB corresponds to which side in \triangle PQR?
BC corresponds to which side in \triangle PQR?
Consider the two similar triangles:
DE corresponds to which side in \triangle LMN?
DC corresponds to which side in \triangle LMN?
In the diagram, JK \parallel MN such that \triangle LJK and \triangle LNM are similar.
Use the correct mathematical symbols to state that the two triangles are similar.
Identify the angle that is equal to:
\angle LJK
\angle LKJ
\angle JLK
Identify the side that corresponds to:
JK
KL
In the diagram, \triangle JIK \sim \triangle LIM.
Identify the angle that is equal to the following. Give a reason for your answer.
\angle IKJ
\angle IJK
Complete the statement: \dfrac{IJ}{IL} = \dfrac{JK}{⬚}
If \triangle ABC \sim \triangle XYZ:
Identify the side that corresponds to:
Identify the angle that corresponds to:
The two given trapeziums are similar:
State the enlargement factor.
Calculate the size of x.
The two given triangles are similar:
Find the missing length y.
The two given triangles are similar:
Calculate the value of x.
Calculate the value of c.
In the diagram, a smaller rectangle is inscribed within a larger rectangle with dimensions as given:
If the length of FG remains fixed, what must be the length of BG so that the two rectangles are similar?
For each pair of similar triangles determine the value of x:
The two given triangles are similar:
Comparing the side lengths of the two triangles, state the ratio of corresponding sides.
Find the value of each pronumeral:
s
n
m
In the diagram, \triangle PQR is similar to \triangle PST:
State the scale factor of enlargement.
Calculate the value of f.
In the diagram, \triangle ABC is similar to \triangle PQR:
Calculate the value of x.
Calculate the value of y.
In the diagram, \triangle AOB is similar to \triangle DOC:
If AB = 5.5, determine the length of CD.
For each of the given diagrams, the two quadrilaterals are similar.
If a = 6\text{ cm}, d = 11\text{ cm} and g = 5\text{ cm}, determine the exact value of k.
If r = 9\text{ m}, s = 17\text{ m} and c = 5\text{ m}, determine the exact value of d.
Council has designed plans for a triangular courtyard in the town square.
The drawing of the courtyard on the plan has dimensions of 4\text{ cm}, 6\text{ cm} and 9\text{ cm}.
The shortest side of the actual courtyard is to be 80\text{ m} long.
Calculate the longest side length of the actual courtyard.
Calculate the middle side length of the actual courtyard.
In the diagram, \triangle ABD and \triangle ECD are similar right-angled triangles, with AE = 14, AB = 6.5 and EC = 1.3.
Find the length of interval ED.
Use this to determine r, the radius of the circle. Round your answer to one decimal place.
For each of the following sets of triangles, state the two triangles that are similar and give the reason for your choice:
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
The pair of triangles in the diagram already have one pair of angles identified as being equal. State another condition required to prove these are similar triangles.
In order to prove the triangles in the following diagram are similar, what extra information is required?
The triangles in the diagram have angles as marked. Is this sufficient information to prove that they are similar triangles?
The pair of triangles in the diagram have side lengths as labelled. In order to prove they are similar triangles, what extra information is required?
For the diagram shown, state the reason why \triangle ABC is similar to \triangle AED.
Use the correct mathematical symbols to state that the two triangles are similar.
Complete the proof to show that these two triangles are similar:
In \triangle ABC and \triangle DFE we have:
\angle ABC = {⬚}, (\text{given})\\ \angle BAC = {⬚}, (⬚) \\ \therefore \triangle ABC \sim {⬚}, \text{ as } {⬚}
Complete the proof to show that these two triangles are similar:
In \triangle ABC \text{ and } \triangle DFE we have:
\dfrac{AC}{DE} = {⬚}
\dfrac{CB}{FE} = {⬚}
\\ \dfrac{AB}{DF} ={⬚} \\ \therefore \triangle ABC \sim {⬚}, \text{ as } {⬚}
\triangle LMN and \triangle LKJ are drawn such that JK \parallel MN.
Prove that \triangle LMN and \triangle LKJ are similar.
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.
Hence determine the ratio of AP to AC.
Consider the following figure:
Prove that \triangle ABE is similar to \triangle BCD.
Prove that \triangle EDB is similar to \triangle BCD.
Can we therefore conclude that \triangle ABE is similar to \triangle EDB?
