Question

1. $\triangle abc \sim \triangle xyz$
2. $\triangle abc \sim \triangle xyz$
3. $\triangle jkl \sim \triangle gkh$
4. $\triangle abc \sim \triangle ade$

Explanation:

Problem 3:

Step1: Find similarity ratio

$\text{Ratio} = \frac{YZ}{BC} = \frac{15}{30} = \frac{1}{2}$

Step2: Solve for $x$

$x = AB \times \frac{1}{2} = 34 \times \frac{1}{2} = 17$

Step3: Solve for $y$

$y = AC \times \frac{1}{2} = 16 \times \frac{1}{2} = 8$

Problem 4:

Step1: Find similarity ratio

$\text{Ratio} = \frac{AB}{XZ} = \frac{14.4}{13} = \frac{72}{65}$

Step2: Solve for $x$

$x = XY \times \frac{72}{65} = 12 \times \frac{72}{65} = \frac{864}{65} \approx 13.29$

Step3: Solve for $y$

$y = YZ \times \frac{72}{65} = 5 \times \frac{72}{65} = \frac{72}{13} \approx 5.54$

Problem 5:

Step1: Find similarity ratio

$\text{Ratio} = \frac{KG}{KJ} = \frac{6}{6+4} = \frac{6}{10} = \frac{3}{5}$

Step2: Solve for $x$

$x = JL \times \frac{3}{5} = 15 \times \frac{3}{5} = 9$

Problem 6:

Step1: Find similarity ratio

$\text{Ratio} = \frac{DE}{BC} = \frac{12.5}{5} = 2.5$

Step2: Solve for $x$

$x = AC \times 2.5 = 4 \times 2.5 = 10$

Step3: Solve for $y$

$y = AB \times 2.5 = 3 \times 2.5 = 7.5$

Answer:

1. $x=17$, $y=8$
2. $x=\frac{864}{65}\approx13.29$, $y=\frac{72}{13}\approx5.54$
3. $x=9$
4. $x=10$, $y=7.5$