Angles Triangles & Polygons Similar & Congruent Polygons Proportions & Similar Polygons Transformations

If m ∠ 1 and m∠ 2 are complementary and the m∠ 1 is 28 °, find m∠2.

62°

If m∠h = 44° and m∠j = 36°, are these angles complementary, supplementary, or neither?

Neither

Classify a 180° angle as right, acute, obtuse, or straight.

Straight

For the given angle find the measure of a supplementary angle and the measure of a complementary angle if possible. 7°

Supplementary = 173° Complementary = 83°

Copy and complete the statements using sometimes, always, or never. Vertical angles are ____________ congruent. Intersecting lines are ________________ perpendicular. When a line intersects two parallel lines, corresponding angles are _______________congruent.

Vertical angles are always congruent. Intersecting lines are sometimes perpendicular. When a line intersects two parallel lines, corresponding angles are always congruent.

Classify the triangle by its angle measures. 68°, 22°, 90°

Right

Classify the triangle by the length of its sides. 5 ft., 14 ft., 11 ft.

Scalene

The measure of one angle of a triangle is 36°. The other two angles are congruent. What are their measures?

Each of the congruent angles has a measure of 72°.

Find the measure of each side of a regular heptagon with a perimeter of 52.5 inches

7.5 inches

Name a quadrilateral that is always a regular polygon.

Square

Fill in the blanks in the following statement. Two polygons are _____________if they have the same shape but not necessarily the same size. ______________________________ are similar polygons that have the same shape and the same size.

Two polygons are similar if they have the same shape but not necessarily the same size. Congruent polygons are similar polygons that have the same shape and the same size.

Do a 9 foot by 12 foot rectangular kitchen and a 12 foot by 15 foot rectangular den have similar shapes?

No

A rectangular painting has a length of 48 inches and a width of 36 inches. A rectangular print of the painting has a length of 32 inches and a width of 24 inches. Are the original and the print similar figures?

Yes

Are any two squares similar? Explain.

Yes. All angles measure 90 °, and the ratio of any side of one square to any side of the other is the same.

△BCD≅ △JKL. If m∠C = 48°, m∠D = 62°, and ∠J corresponds to ∠B, what is m∠J?

70 °

The ratio of corresponding side lengths of two similar polygons is 5/6. How long is a side of the larger polygon corresponding to a side of length 20 in the smaller.

24

Muffy photographs a giraffe that is 15 feet tall, with a 12 foot shadow. If Muffy’s shadow is 4 feet long, how tall is she?

5 ft.

A man who is 6 feet tall stands next to a street sign. The man’s shadow is 4 feet long. At the same time, the sign’s shadow is 6 feet long. Write and solve a proportion to find the height of the sign.

6/4 = x/6 x = 9 ft.

A rectangular movie poster has a length of 28 inches and width of 22 inches. A print of the poster is similar to the original and has a length of 14 inches. What is the width of the print?

11 inches

A 7 ft. tall welcome sign in a city park casts a shadow that is 2 feet long. At the same time, a monument in the park casts a shadow that is 16 feet long. Draw a diagram to represent the situation. Then find the height of the monument.

56 ft.

Fill in the missing terms. In a ____________, or slide, each point of a figure is moved the same distance in the same direction. In a ______________, or flip, a figure is reflected in a line called the ______ ____ ________________, creating a mirror image of the figure.

In a translation, or slide, each point of a figure is moved the same distance in the same direction. In a reflection, or flip, a figure is reflected in a line called the line of reflection, creating a mirror image of the figure.

A fixed camera snaps two pictures of a race car, one just before crossing the finish line and one just after. What kind of transformation does the car’s position in the pictures represent?

Translation

Describe the translation of a figure 6 units to the right and 1 unit down using coordinate notation.

(x,y) → (x + 6, y – 1)

Find the coordinates of the vertices A(-1,3), B(2,1), C(6,4) of a triangle after the rotation (x,y) → (-y,x).

A΄(-3,-1) B΄(-1,2) C΄(-4,6)

Draw quadrilateral QRST with vertices Q(3,2), R(4,5), S(-2,4), and T(-1,1). Then find the coordinates of the vertices of the image after it is reflected in the x- axis.

Q΄(3,-2) R΄(4,-5) S΄(-2,-4) T΄ (-1,-1)