Question

1. in each of the following cases, indicate if the given figures are similar.

a)

b)

c)

d)

1. determine the value of ( x ) in each of the following cases, given that the figures are similar.

a)

b)

c)

d)

Explanation:

For Question 6:

a) Check side ratios: $\frac{2}{3}
eq \frac{4}{8}$ (or $\frac{1}{2}$), so sides are not proportional.
b) All squares have equal angles (90°) and proportional sides ($\frac{3}{4}$ is the ratio), so they are similar.
c) First triangle: right-angled, one acute 36°, so the other is 54°. Second triangle: right-angled, one acute 54°, so angles match, making them similar.
d) Check side ratios: $\frac{2}{3}
eq \frac{4.2}{8}$ ($\frac{2}{3} \approx 0.67$, $\frac{4.2}{8}=0.525$), so sides are not proportional.

Step1: Find similarity ratio (a)

The ratio of corresponding sides is $\frac{4.2}{3} = 1.4$.

Step2: Solve for $x$ (a)

Multiply the corresponding side by the ratio: $x = 4 \times 1.4$
$x = 5.6$

Step3: Find similarity ratio (b)

The ratio of corresponding sides is $\frac{7.8}{6} = 1.3$.

Step4: Solve for $x$ (b)

Multiply the corresponding side by the ratio: $x = 9 \times 1.3$
$x = 11.7$

Step5: Find similarity ratio (c)

The ratio of corresponding sides is $\frac{3.75}{5} = 0.75$.

Step6: Solve for $x$ (c)

Multiply the corresponding side by the ratio: $x = 4 \times 0.75$
$x = 3$

Step7: Find similarity ratio (d)

The ratio of corresponding sides is $\frac{3.6}{3} = 1.2$.

Step8: Solve for $x$ (d)

Multiply the corresponding side by the ratio: $x = 5 \times 1.2$
$x = 6$

Answer:

a) Not similar
b) Similar
c) Similar
d) Not similar

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For Question 7: