Quiz about Plane Geometry Act

Question 1

If the figure, ABCD is a trapezoid, E lies on $$\overline{AD}$$ , and angle measures are as marked. What is the measure of $$\angle BDC$$ ?

Accepted Answer

$$45\degree$$

Answer

$$15\degree$$

Answer

$$25\degree$$

Answer

$$30\degree$$

Answer

$$35\degree$$

Question 2

A triangle with a perimeter of 66 inches has one side that is 16 inches long. The lengths of the other two sides have a ratio of 2:3. What is the length, in inches, of the $$longest$$ side of the triangle?

Accepted Answer

30

Answer

16

Answer

20

Answer

40

Answer

50

Question 3

In the figure, B is on $$\overline{AC,}$$ E is on $$\overline{DF,}$$ $$\overline{AC}$$ is parallel to $$\overline{DF,}$$ and $$\overline{BE}$$ is congruent to $$\overline{BF.}$$ Wha tis the measure of $$\angle DEB?$$

Accepted Answer

$$145\degree$$

Answer

$$35\degree$$

Answer

$$135\degree$$

Answer

$$155\degree$$

Answer

$$215\degree$$

Question 4

In $$\Delta ABC$$ D, E, and F are points on $$\overline{AB,}$$ $$\overline{BC,}$$ and $$\overline{AC,}$$ respectively, and $$\overline{DF}$$ is congruent to $$\overline{EF.}$$ What is the sum of the measures of the angles marked x and y?

Accepted Answer

$$90\degree$$

Answer

$$40\degree$$

Answer

$$80\degree$$

Answer

$$100\degree$$

Answer

$$130\degree$$

Question 5

Which of the following lists gives 2 of the 3 interior angle measurements of a triangle for which the third angle measurement would be equal to 1 of the given measurements?

Accepted Answer

$$40\degree,\ 100\degree$$

Answer

$$20\degree,\ 40\degree$$

Answer

$$30\degree,\ 60\degree$$

Answer

$$45\degree,\ 120\degree$$

Answer

$$50\degree,\ 60\degree$$

Question 6

A ladder is 10 ft long and reaches 8 ft up a wall, as shown in the figure. How many feet is the bottom of the ladder from the base of the wall?

Accepted Answer

6

Answer

2

Answer

3

Answer

$$\sqrt[]{2}$$

Answer

$$\sqrt[]{164}$$

Question 7

WHich of the following sets of 3 numbers could be the side lengths, in meters, of a $$30\degree\ -60\degree\ -90\degree$$ triangle?

Accepted Answer

$$1,\ \sqrt[]{3},\ 2$$

Answer

1, 1, 1

Answer

$$1,\ 1,\ \sqrt[]{2}$$

Answer

$$1,\ \sqrt[]{2},\ \sqrt[]{2}$$

Answer

$$1,\ \sqrt[]{2},\ \sqrt[]{3}$$

Question 8

In the figure, ABCD is a square and E, F, G, and H are the midpoints of its sides. If $$\overline{AB}\ =12\ inches,$$ what is the perimeter of EFGH, in iches?

Accepted Answer

$$24\sqrt[]{2}$$

Answer

24

Answer

$$36\sqrt[]{2}$$

Answer

$$48\sqrt[]{2}$$

Answer

72

Question 9

In the figure shown, each pair of intersecting line segments meets at a right angle, and all the lengths given are in inches. WHat is the perimeter, in inches, of the figure?

Accepted Answer

80

Answer

40

Answer

52

Answer

56

Answer

66

Question 10

THe trapezoid is divided into 2 triangles and 1 rectangle. Lengths are given in inches. What is the combined area, in square inches, of the 2 shaded triangles?

Accepted Answer

6

Answer

4

Answer

9

Answer

12

Answer

18

Question 11

The ratio of the radii of two circles is 4:9. What is the ratio of their circumferences?

Accepted Answer

4:9

Answer

2:3

Answer

16:81

Answer

Answer

$$9:18\pi$$

Question 12

A formula for the volume V of a sphere is $$V=\frac{4}{3}\pi^3.$$ If the radius of a spherical rubber ball is $$1\frac{1}{4},$$ what is its volume to the nearest cubic inch?

Accepted Answer

8

Answer

5

Answer

7

Answer

16

Answer

65

Question 13

For right triangle $$\Delta RST,$$ what is tan R?

Accepted Answer

$$\frac{r}{t}$$

Answer

$$\frac{r}{s}$$

Answer

$$\frac{t}{r}$$

Answer

$$\frac{t}{s}$$

Answer

$$\frac{s}{t}$$

Question 14

If $$\sin heta=-\frac{3}{5}$$ and $$\pi< heta<\frac{3\pi}{2},\ then\ an heta=?$$

Accepted Answer

$$\frac{3}{4}$$

Answer

$$-\frac{5}{4}$$

Answer

$$-\frac{3}{4}$$

Answer

$$-\frac{3}{5}$$

Answer

$$\frac{4}{5}$$

Question 15

In the figure, lines m and n are parallel, transversals r and s intersect to form an angle of measure $$x\degree$$ , and 2 other angle measures are as marked. What is the value of x?

Accepted Answer

35

Answer

15

Answer

25

Answer

65

Plane Geometry Act

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