A focused Grade 7 learning session for Similar Figures and Proportions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving similar figures and proportions.
Similar Figures and Proportions is part of Grade 7 Geometry and Scale. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of similar figures and proportions using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Similar Figures and Proportions, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving similar figures and proportions.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Two triangles are similar. The sides of the smaller triangle are \(3\), \(4\), and \(5\). The longest side of the larger triangle is \(15\). What is the length of the shortest side of the larger triangle?
Answer C: \(9\)
The scale factor is \(15\div5=3\). The shortest side of the larger triangle is \(3\times3=9\).
Triangles 1 and 2 are similar right triangles. What is the length of the missing side in Triangle 2?
Answer C: \(9\) cm
The scale factor from Triangle 1 to Triangle 2 is \(\frac{12}{8}=1.5\). The missing side is \(6 \times 1.5 = 9\) cm.
Two similar rectangles have a scale factor of \(2:5\). If the smaller rectangle has a perimeter of \(28\) inches, what is the perimeter of the larger rectangle?
Answer C: \(70\) inches
The perimeter scales with the same factor as the sides. If the scale factor is \(2:5\), then \(\frac{\text{smaller}}{\text{larger}}=\frac{2}{5}\), so \(\text{larger}=28\times\frac{5}{2}=70\) inches.
Two similar triangles have corresponding sides in the ratio \(3:7\). If an angle in the smaller triangle measures 45°, what is the measure of the corresponding angle in the larger triangle?
Answer A: 45°
Corresponding angles in similar figures are congruent, regardless of the scale factor. The corresponding angle is also 45°.
The two rectangles are similar. What is the scale factor from the original to the scaled rectangle?
Answer B: \(1.4\)
The scale factor is \(\frac{28}{20}=1.4\). We can verify: \(10 \times 1.4 = 14\) \checkmark
Two similar isosceles triangles have areas in the ratio \(4:25\). What is the ratio of their corresponding sides?
Answer A: \(2:5\)
Area scales by the square of the linear scale factor. If areas are \(4:25\), then the linear scale factor is \(\sqrt{4}:\sqrt{25}=2:5\).
In a map, a scale of \(1\) inch \(= 50\) miles is used. On the map, two cities are \(3.5\) inches apart. What is the actual distance between the cities?
Answer B: \(175\) miles
Using the scale: \(3.5 \text{ inches} \times 50 \text{ miles/inch} = 175\) miles.
Two similar right triangles are shown. The left triangle has legs \(5\) ft (horizontal) and \(4\) ft (vertical). The right triangle has a vertical leg of \(3.2\) ft. Find the horizontal leg of the right triangle.
Answer C: \(4\) ft
The vertical leg of the left triangle is \(4\) ft, and the right triangle's vertical leg is \(3.2\) ft. Scale factor \(= \frac{3.2}{4}=0.8\). The horizontal leg of the right triangle is \(5 \times 0.8 = 4\) ft.
A photograph has dimensions \(6\) inches by \(8\) inches. It is enlarged so that the longer side becomes \(20\) inches. What is the length of the shorter side after enlargement?
Answer C: \(15\) inches
The scale factor is \(\frac{20}{8}=2.5\). The shorter side is \(6 \times 2.5 = 15\) inches.
The figure on the left is scaled by a factor of \(1.5\) to create the figure on the right. If the height of the left figure is \(2\) cm, what is the height of the scaled figure?
Answer C: \(3\) cm
All linear dimensions scale by the scale factor. Height \(= 2 \times 1.5 = 3\) cm.
If \(\frac{x}{6}=\frac{12}{8}\), what is the value of \(x\)?
Answer C: \(9\)
Cross-multiply: \(8x = 12 \times 6 = 72\), so \(x = \frac{72}{8} = 9\).
