Question

1. $\triangle abc sim \triangle xyz$

find side length x.
a) 30
b) 25
c) 15
d) 40

1. $\triangle jkl sim \triangle gkh$

find side length x.
a) 22.5
b) 10
c) 9
d) 7.5
17.
are the triangles similar?
a) yes
b) no

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
19.
the triangles are similar, solve for the question mark.
a) 8
b) 12.5
c) 18
d) 24
20.
to measure the distance across a pond, a surveyor locates points a, b, c, d, and e as shown. find ab to the nearest meter?
a) 10
b) 12
c) 15
d) 18

Explanation:

Step1: Set up similarity proportion (Q15)

$\frac{40}{20} = \frac{50}{x}$

Step2: Solve for $x$ (Q15)

$x = \frac{50 \times 20}{40} = 25$

Step3: Set up similarity proportion (Q16)

$\frac{6}{12} = \frac{x}{15}$

Step4: Solve for $x$ (Q16)

$x = \frac{6 \times 15}{12} = 7.5$

Step5: Check triangle angles (Q17)

For $\triangle ABC$: $\angle A = 180^\circ - 90^\circ - 35^\circ = 55^\circ$; $\triangle DEF$ has $\angle D=55^\circ$, right angles match. AA similarity applies.

Step6: Recall similar polygon rules (Q18)

By definition, similar polygons have proportional corresponding sides and congruent corresponding angles.

Step7: Set up similarity proportion (Q19)

$\frac{10}{15} = \frac{12}{?}$

Step8: Solve for unknown side (Q19)

$? = \frac{15 \times 12}{10} = 18$

Step9: Set up similarity proportion (Q20)

$\frac{5}{5+5} = \frac{9}{AB}$

Step10: Solve for $AB$ (Q20)

$AB = \frac{9 \times 10}{5} = 18$

Answer:

1. b) 25
2. d) 7.5
3. a) Yes
4. b) proportional, congruent
5. c) 18
6. d) 18