8th grade summer midterm-

If the two triangles shown are congruent, what is true of the two triangles?

• Each side of the first triangle has a congruent match on the second triangle.

• The two triangles are right triangles with congruent sides and angles.

• The two triangles are obtuse.

• The two triangles are equilateral.

Describe the transformation. (Refer to the diagram of two triangles on a coordinate grid)

• translation 4 units to the right

• reflection across the x-axis

• reflection across the line y = x

• reflection across the y-axis

Given that the triangles shown are isosceles, which set shows two similar triangles?

• Set A: △ABC and △DEF

• Set B: △GHI and △JKL

• Set C: △MNO and △PQR

• Set D: △STU and △VWX

Which pair of triangles are similar?

• Triangles with sides 5 cm, 3 cm and 15 cm, 9 cm

• Triangles with sides 6 cm, 5 cm and 7 cm, 6 cm

• Triangles with sides 8 cm, 5 cm and 9 cm, 6 cm

• Triangles with sides 8 cm, 3 cm and 9 cm, 6 cm

As shown in the graph, ΔGHI ≅ ΔG'H'I', since this is a vertical shift, and ΔG'H'I' ≅ ΔG''H''I'', since this is a horizontal shift. What translation can we use to directly show that triangles GHI and G''H''I'' are congruent?

• (x, y) → (x + 2, y + 2)

• (x, y) → (x + 3, y - 4)

• (x, y) → (x - 3, y + 1)

• (x, y) → (x + 4, y - 5)

Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.

• translate triangle A 4 units down and then rotate triangle A 180° counterclockwise about the origin

• reflect triangle A across the y-axis and then translate triangle A 5 units down

• reflect triangle A across the x-axis and then rotate triangle A 90° counterclockwise about the origin

• reflect triangle A across the x-axis and then reflect triangle A across the y-axis

Which transformation can be used to map ABCD onto EFGH and to confirm that the figures are congruent?

• A translation

• A dilation

• A reflection

• A rotation

Refer to the diagram of rectangles ABCD and EFGH. Which transformation maps rectangle ABCD to rectangle EFGH?

• ABCD can be mapped to EFGH with a translation right 4 units and down 4 units.

• ABCD can be mapped to EFGH with a translation right 4 units and up 4 units.

• ABCD can be mapped to EFGH with a translation left 4 units and up 4 units.

• ABCD can be mapped to EFGH with a translation left 4 units and down 4 units.

Which sequence of transformations will only produce a figure similar to but not congruent to the figure ABCD?

• ABCD is translated 4 units left, 2 units up, and then reflected across the y-axis.

• ABCD is rotated 180° clockwise about the origin and then translated 3 units right.

• ABCD is translated 2 units to the right and then reflected across the x-axis.

• ABCD is dilated by a scale factor 3 and then rotated 90° clockwise about the origin.

Which transformation confirms that rectangle ABCD and rectangle EFGH are similar?

• A dilation

• A translation

• A rotation

• A reflection