Free Printable Algebra 1 / Geometry A Homework

1.

In similar Polygons, corresponding sides are ___ and corresponding angles are ___. (Fill in the blanks)

a)

congruent, proportional

b)

proportional, congruent

c)

congruent, congruent

d)

proportional, proportional

2.

Choose the similarity statement for the triangles.

a)

ΔMNL ∼ ΔOPQ

b)

ΔNOM ∼ ΔPQL

c)

ΔLMN ∼ ΔPQO

d)

ΔMLN ∼ ΔPQO

3.

Figure A is reduced to Figure B. Find the scale factor.

a)

4

b)

1/4

c)

3

d)

1/3

4.

Given: $\Delta PQR\sim\Delta XYZ$

What is the measure of $\angle Q$ ?

a)

70 degrees

b)

30 degrees

c)

40 degrees

d)

25 degrees

5.

State the postulate that proves these triangles are similar.

a)

SSS

b)

AA

c)

SAS

d)

Not similar

6.

How do these triangles appear to be similar?

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

7.

How do these triangles appear to be similar?

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

8.

What similarity theorem would you use to prove these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

BUCK∼

9.

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

10.

a)

7

b)

12

c)

6

d)

4

11.

Find x AND the measure of line segment MN.

a)

X = 14

MN = 15

b)

X = 12

MN = 13

c)

X = 15

MN = 28

d)

X = 18

MN = 52

12.

Are the following similar? Why or why not?

a)

Yes

b)

No, the corresponding angles are not equal.

c)

No, the ratios of the corresponding sides are not equal.

13.

What is the scale factor of the bigger triangle to the smaller triangle?

a)

1.25

b)

1.5

c)

2

d)

2.5

14.

In the figure shown, which of the following ratio has the same value as $\frac{AB}{BC}$ ?

a)

$\frac{BD}{DC}$

b)

$\frac{BC}{AC}$

c)

$\frac{AD}{BD}$

d)

$\frac{DC}{BC}$

15.

Which of the other triangles is similar to ΔABC

a)

b)

c)

d)

None of the above

16.

Which triangles are similar to triangle A?

a)

B

b)

C

c)

Both

d)

None

17.

Select the proportion that shows the Triangle Proportionality Theorem.

a)

$\frac{6}{27}=\frac{7}{x}$

b)

$\frac{6}{21}=\frac{7}{x}$

c)

$\frac{7}{6}=\frac{x}{27}$

d)

$\frac{21}{6}=\frac{7}{x}$

18.

Find x.

a)

147

b)

21

c)

24.5

d)

26.5

19.

Which of the following proportions could be used to find the missing length indicated?

a)

$\frac{x}{18}=\frac{20}{28}$

b)

$\frac{x}{18}=\frac{8}{20}$

c)

$\frac{18}{x+18}=\frac{8}{28}$

d)

$\frac{x}{x+18}=\frac{8}{28}$

20.

Find the missing length indicated.

Write down your work.

a)

30

b)

25

c)

45

d)

50

21.

Find the perimeter of $\Delta MNP$ .

a)

110

b)

120

c)

130

d)

140

22.

Find the measure of angle SUR

a)

55 degrees

b)

125 degrees

c)

180 degrees

d)

not enough information

23.

QR is a midsegment of triangle BCD. Solve for the value of x.

a)

11

b)

18

c)

9

d)

-7

24.

If DG = 2, DF = 8, and FH is $\frac{3}{4}$ of EF. Is GH // DE?

a)

Yes

b)

No

25.

If $AE\parallel BF\parallel CG$ , select all correct answers.

a)

$\frac{AB}{BC}=\frac{EF}{FG}$

b)

$\frac{BC}{AB}=\frac{EF}{FG}$

c)

$\frac{AC}{BC}=\frac{EG}{FG}$

d)

$\frac{AB}{EF}=\frac{BC}{FG}$

26.

If $AE\parallel BF\parallel CG$ and $AB\cong BC$ , select all correct answers.

a)

$EF\cong AB$

b)

$EF\cong FG$

c)

$BC\cong FG$

d)

$\frac{AB}{EF}=\frac{BC}{FG}$

27.

Solve for x

a)

16

b)

13.9

c)

15.3

d)

11

28.

Solve for x

a)

10

b)

-6

c)

26

d)

14

29.

If two triangles are similar, select all correct ratios that are proportional to the scale factor (the ratio of corresponding side lengths).

a)

Perimeter

b)

Angle Bisector

c)

Median

d)

Area

e)

Altitude

30.

ΔABC ~ ΔWXY. If AC = 10, WY = 8, and YZ = 12, what is the length of CD?

a)

9

b)

12

c)

15

d)

18

31.

ΔKLM ~ ΔQSR. If KM = 12, QS = 18, and LP = 8, what is the length of RT?

a)

8

b)

12

c)

15

d)

18

32.

The ratio of the corresponding sides of two similar triangles is 3:5. What is the ratio of the perimeters of these triangles?

a)

5:3

b)

9:25

c)

3:5

d)

6:10

33.

If the scale factor of lengths of similar figures is $k$ , what is the scale factor of areas of similar figures?

a)

$k$

b)

$k^2$

c)

$k^3$

d)

$\frac{1}{k}$

34.

If the scale factor of the side length is $\frac{3}{2}$ , then what is the scale factor of the corresponding areas?

a)

$\frac{2}{3}$

b)

$\frac{3}{2}$

c)

$\frac{4}{9}$

d)

$\frac{9}{4}$

35.

If the ratio of areas is 9:100, then the ratio of the corresponding side length is

a)

3:10

b)

9:100

c)

81:10000

d)

27:1000

36.

A quadrilateral FGHI is similar to quadrilateral F’G’H’I’. Given FI = 12 cm, F’I’ = 8 cm, and the area of FGHI = 48 cm², determine the area of F’G’H’I’.

a)

12.5

b)

21.3

c)

25.2

d)

31.5

37.

The child size is simply a dilation of the adult size pattern. The first adult panel measures 16 inches across and uses an area of 200 square inches of denim fabric. The first child size panel measures 12 inches across. How much denim fabric will be required for the first child size panel?

a)

90

b)

112.5

c)

120.5

d)

135

38.

If $DE\parallel BC$ , $AD=6$ , $DB=3$ and area of $\Delta ABC$ is 18, what is the area of $\Delta ADE$ ?

a)

4

b)

8

c)

12

d)

15

39.

If $DE\parallel BC$ , $AE=8$ , $EC=4$ and area of $\Delta ABC$ is 27, what is the area of the trapzoid BCED ?

a)

9

b)

12

c)

15

d)

18

40.

What is the midpoint between (-4,4) and (-2,2)?

a)

(3,2)

b)

(-3,3)

c)

(4,5)

d)

(6,7)

Algebra 1 / Geometry A Homework - April 18, 2023

Total questions: 40

Worksheet time: 10hrs 0mins

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