Congruence, Dilations and Similarity: Grade 8 Math Quiz – PDF Download
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
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Question 1
Which transformation produces an image that is NOT congruent to the original figure?
AA reflection across the \(x\)-axis
BA rotation of \(90^{\circ}\) about the origin
CA translation 3 units left
DA 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.
AA reflection across the \(x\)-axis
BA reflection across the \(y\)-axis
CA translation 5 units left and 6 units down
DA rotation of \(180^{\circ}\) about the origin
Question 6
A triangle is dilated with scale factor 3. Which quantity stays the same?
AEach side length
BEach angle measure
CThe perimeter
DThe 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?
A3 in by 5 in and 6 in by 8 in
B4 in by 6 in and 7 in by 9 in
C3 in by 5 in and 9 in by 15 in
D2 in by 3 in and 4 in by 7 in
Question 9
Which sequence maps triangle \(ABC\) onto triangle \(DEF\)?
Triangles \(ABC\) and \(DEF\).
ADilate by 2, then reflect across the \(y\)-axis
BDilate by 2, then reflect across the \(x\)-axis
CDilate by \(\frac{1}{2}\), then reflect across the \(y\)-axis
DTranslate 3 units left and 1 unit up
Question 10
Which statement correctly defines congruent figures?
AThe figures have the same shape but may have different sizes
BOne figure can be mapped onto the other by a sequence of rotations, reflections and translations
COne figure is a dilation of the other with scale factor 2
DThe figures have the same area but may have different shapes
🎉 Quiz complete!
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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 \((y,-x)\).
