Congruence
Determine if the two figures are congruent by using transformations. Explain your reasoning.
congruent; figure reflected over vertical line then translated
Determine whether the pair of polygons is similar using properties of similar polygons. Explain your reasoning
similar; The corresponding angles are congruent and the corresponding sides are proportional, k=2
A flag pole casts a 5 foot shadow while a nearby sign post casts a 1 1/4 foot shadow. Find the height of the flagpole if the sign post is 4 feet high.
16 ft
Graph each pair of similar triangles. Then write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
EFG with vertices E(1,9), F(1,5), and G(2,5); GHI with vertices G(2,5), H(1,2), and I(3,1)
EF / FG = GH / HI , or - 4 / 1
The length of a rectangle is 9 inches and the perimeter is 30. A similar rectangle has a length of 6 inches. What is the perimeter of the second rectangle?
20 in.
Determine if the two figures are congruent by using transformations. Explain your reasoning.
congruent; figure rotated 90 clockwise then translated
Which pair of polygons is similar?
C
A statue casts a shadow 25 feet long. A boy standing next to the statue is 4.5 feet tall and casts a shadow that is 3.6 feet long. How tall is the statue?
31.25 ft
Graph each pair of similar triangles. Then write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value
RST with vertices R(1,6), S(1,-6), and T(-3,-6); UVW with vertices U(-1,0), V(-1,-3), and W(-2,-3)
RS / ST = UV / VW, or 3 / 1
The length of a rectangle is 45 inches and the width is 8 inches. A similar rectangle has a width of 24 inches. What is the perimeter of the second rectangle?
318 in
The triangles below are congruent.
Write congruency statements comparing the corresponding parts
Corresponding angles: ∠A congruent ∠F; ∠B congruent ∠G; ∠C congruent ∠H; Corresponding sides AB congruent FG; BC congruent GH; AC congruent FH
Determine whether the triangles are similar. If so, write a similarity statement
similar; PQR ˜ TUV; AA Similarity
Determine whether the triangles are similar. If so, write a similarity statemen
similar; ∠C congruent ∠E, ∠ABC congruent ∠EBD (vertical angles) ;ABC ˜ DBE
Use the similar slope triangles to show that the slope of the line is the same between any two distinct points on the line.
AB / BC = -1 / 1 = - 1 and FG / GH = -2 / 2 = -1
A triangle has a side length of 4 inches and an area of 18 square inches and a larger similar triangle has a corresponding side length of 8 inches. Find the area of the larger triangle
72 in2
Describe a series of transformations that maps triangle ABC onto triangle FGH
rotation 180° then translation
Determine if the two figures are similar by using transformations. Explain your reasoning.
not similar; The ratios comparing the corresponding side lengths are not equal so a dilation did not occur.
Mitzi is 64 inches tall and casts a 48 inch shadow. Her daughter, who is standing next to her, casts a 30 inch shadow. How tall is her daughter?
40 in
Write a proportion comparing the rise to the run for each of the similar slope triangles shown at the right. Then find the numeric value.
AB / BC = CD / DE -2 / 2 = -4 / 4 = -1
Two rectangles are similar. The length and width of the first rectangle is 4 meters by 5 meters. The second rectangle is similar by a scale factor 4. What is the area of the second rectangle?
320 m2
Triangle PQR has vertices at (0, 0), (2, 0), and (0, 2). a. Graph PQR.
b. Reflect PQR over the x-axis, then dilate it by a scale factor of 2. Label the vertices of the image PQR.
c. Are the two triangles congruent? Justify your response.
no; The dilation enlarged the figure.
The length of a rectangle is 18 centimeters and the width is 6 centimeters. A similar rectangle has a width of 2 centimeters. What is the length of the second rectangle?
6 cm
Dominic is 72 inches tall and casts a 60 inch shadow. His son, who is standing next to him, casts a 50 inch shadow. How tall is his son?
60 in
Graph each pair of similar triangles. Then write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
DEF with vertices D(-6,5), E(-6,2), and F(-2,2); FMW with vertices F(-2,2), M(-2,-4), and W(6,-4)
DE / EF = FM / MW, or -3 / 4
A rectangular shaped flower garden has a length of 5 yards and an area of 15 square yards. A neighbor’s flower garden is similar and has a length of 7 yards. What is the area of the neighbor’s flower garden? Round your answer to the nearest whole number.
29 yd2