Grade 8 Congruence Similarity Quiz – Free PDF

Contents

This grade 8 congruence similarity quiz asks 10 multiple-choice questions on congruence, dilations and similarity, and each answer comes with a short explanation.

Ten multiple-choice questions check rigid motions, coordinate rules, dilations and similar figures. Each question has exactly one correct answer. Read the explanation after each choice to learn the typical mistake.

Grade 8Common Core: 8.G.A.2 · 8.G.A.3 · 8.G.A.4

🎯 Congruence, Dilations and Similarity – Grade 8 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

Which transformation produces an image that is NOT congruent to the original figure?

A A reflection across the \(x\)-axis

B A rotation of \(90^{\circ}\) about the origin

C A translation 3 units left

D A dilation with scale factor 2

Question 2

Which rule describes a reflection across the \(y\)-axis?

A \((x,y)\to(x,-y)\)

B \((x,y)\to(-x,-y)\)

C \((x,y)\to(-x,y)\)

D \((x,y)\to(y,x)\)

Question 3

What is the image of \((3,-1)\) after a \(90^{\circ}\) counterclockwise rotation about the origin?

A \((-1,-3)\)

B \((-3,1)\)

C \((-1,3)\)

D \((1,3)\)

Question 4

A dilation about the origin has scale factor \(\frac{1}{2}\). What is the image of \((6,-4)\)?

A \((3,-2)\)

B \((12,-8)\)

C \((3,-4)\)

D \((-3,2)\)

Question 5

Which single transformation maps triangle \(ABC\) onto triangle \(A^{\prime}B^{\prime}C^{\prime}\)?

Triangle \(ABC\) and its image.

A A reflection across the \(x\)-axis

B A reflection across the \(y\)-axis

C A translation 5 units left and 6 units down

D A rotation of \(180^{\circ}\) about the origin

Question 6

A triangle is dilated with scale factor 3. Which quantity stays the same?

A Each side length

B Each angle measure

C The perimeter

D The distance from each vertex to the origin

Question 7

The two triangles are similar. What is the scale factor from the small triangle to the large one?

The two triangles, drawn to scale.

A \(\frac{5}{2}\)

B \(\frac{2}{5}\)

C \(6\)

D \(\frac{3}{2}\)

Question 8

Which pair of rectangles is similar?

A 3 in by 5 in and 6 in by 8 in

B 4 in by 6 in and 7 in by 9 in

C 3 in by 5 in and 9 in by 15 in

D 2 in by 3 in and 4 in by 7 in

Question 9

Which sequence maps triangle \(ABC\) onto triangle \(DEF\)?

Triangles \(ABC\) and \(DEF\).

A Dilate by 2, then reflect across the \(y\)-axis

B Dilate by 2, then reflect across the \(x\)-axis

C Dilate by \(\frac{1}{2}\), then reflect across the \(y\)-axis

D Translate 3 units left and 1 unit up

Question 10

Which statement correctly defines congruent figures?

A The figures have the same shape but may have different sizes

B One figure can be mapped onto the other by a sequence of rotations, reflections and translations

C One figure is a dilation of the other with scale factor 2

D The figures have the same area but may have different shapes

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards 8.G.A.2, 8.G.A.3 and 8.G.A.4: congruence, coordinates under transformations, and similarity.
Rigid motions (translation, reflection, rotation) keep lengths and angle measures.
Dilation about the origin: \((x,y)\to(kx,ky)\); lengths scale by \(k\), angles do not change.
Similar figures: a sequence of rigid motions and dilations maps one onto the other.
Rotation rules about the origin: \(90^{\circ}\) is \((-y,x)\), \(180^{\circ}\) is \((-x,-y)\), \(270^{\circ}\) is \((y,-x)\).