Congruence, Dilations and Similarity: Grade 8 Math Test – PDF Download

Grade 8 Congruence Similarity Test: questions 1–5

Question 1: Move a point (2 points)

The point \(P(-3,5)\) is moved.

1. Translate \(P\) 6 units right and 4 units down. Write the image. (1 point)
2. Reflect \(P\) across the \(x\)-axis. Write the image. (1 point)

Question 2: Rotate a point (2 points)

The point \(Q(4,-2)\) is rotated about the origin.

1. Rotate \(Q\) \(90^{\circ}\) counterclockwise. Write the image. (1 point)
2. Rotate \(Q\) \(180^{\circ}\). Write the image. (1 point)

Question 3: Dilate two points (2 points)

Find the image of each point under a dilation about the origin.

1. \(R(6,-9)\) with scale factor \(\frac{1}{3}\) (1 point)
2. \(S(-2,5)\) with scale factor 4 (1 point)

Question 4: Reflect and compare (3 points)

Triangle \(ABC\) is reflected across the \(y\)-axis to form triangle \(A^{\prime}B^{\prime}C^{\prime}\).

1. Write the coordinates of \(A^{\prime}\), \(B^{\prime}\) and \(C^{\prime}\). (2 points)
2. Is triangle \(A^{\prime}B^{\prime}C^{\prime}\) congruent to triangle \(ABC\)? Explain. (1 point)

Question 5: Dilation of a triangle (2 points)

A right triangle has sides \(5\text{ ft}\), \(12\text{ ft}\) and \(13\text{ ft}\). It is dilated with scale factor 3.

1. Find the three side lengths of the image. (1 point)
2. Find the measure of the right angle in the image. Explain. (1 point)

Grade 8 Congruence Similarity Test: questions 6–9

Question 6: Find a scale factor (2 points)

A dilation about the origin sends \(A(3,-2)\) to \(A^{\prime}(12,-8)\).

1. Find the scale factor. (1 point)
2. Find the image of \(B(-5,6)\). (1 point)

Question 7: Show similarity (3 points)

Triangle \(ABC\) and triangle \(DEF\) are shown.

1. Describe a sequence of a dilation about the origin and one rigid motion that maps \(ABC\) onto \(DEF\). (2 points)
2. Are the triangles similar, congruent, both or neither? Explain. (1 point)

Question 8: Similar rectangles (2 points)

A rectangle is 6 inches wide and 9 inches tall.

1. Is it similar to a rectangle that is 8 inches wide and 12 inches tall? Explain. (1 point)
2. Is it similar to a rectangle that is 10 inches wide and 16 inches tall? Explain. (1 point)

Question 9: Two rigid motions (2 points)

Triangle \(XYZ\) has vertices \(X(1,2)\), \(Y(4,2)\), \(Z(4,6)\). It is translated 2 units left and 3 units down, and the result is reflected across the \(y\)-axis.

1. Write the vertices of the final image. (1 point)
2. Side \(XZ\) has length 5. What is the length of the matching side in the final image? Explain. (1 point)

How to use this grade 8 congruence similarity test

Take this grade 8 congruence similarity test without notes, then grade it with the test answer key out of 20 points.

⬇ Download the Grade 8 Congruence, Dilations and Similarity test (PDF, 95 KB)

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