A focused Grade 7 learning session for Drawing Geometric Figures with Given Conditions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving drawing geometric figures with given conditions.
Drawing Geometric Figures with Given Conditions 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 drawing geometric figures with given conditions 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 Drawing Geometric Figures with Given Conditions, 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 drawing geometric figures with given conditions.
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.
How many distinct triangles can be drawn with side lengths \(5\) cm, \(7\) cm, and \(12\) cm?
Answer A: \(0\)
By the Triangle Inequality, \(5+7=12\). Since the sum of two sides must be STRICTLY greater than the third, no triangle exists.
A triangle has side lengths of \(6\) cm and \(9\) cm. Which length CANNOT be the third side?
Answer C: \(16\) cm
By Triangle Inequality, \(|9-6| < c < 9+6\) gives \(3 < c < 15\). Choice C (\(16\) cm) exceeds \(15\), so it fails. A: \(5 > 3\) ✓. B: \(10 < 15\) ✓. D: \(8 < 15\) ✓.
Greta wants to draw a triangle with sides \(5\) m and \(12\) m. If the third side is a whole number of meters, what is the maximum possible length?
Answer B: \(16\) m
By Triangle Inequality, the third side \(c\) must satisfy \(5+12 > c\), so \(c < 17\). The greatest whole number less than \(17\) is \(16\).
What is the minimum possible length (in whole meters) for the third side of a triangle with sides \(5\) m and \(12\) m?
Answer C: \(8\) m
The third side \(c\) must satisfy \(|12-5| < c\), so \(c > 7\). The smallest whole number greater than \(7\) is \(8\).
Can a triangle be drawn with side lengths \(2.5\) cm, \(3.5\) cm, and \(6\) cm?
Answer C: No, because \(2.5 + 3.5 = 6\)
The sum of the two smaller sides equals (not exceeds) the largest side, violating the strict Triangle Inequality.
Which set of conditions does NOT uniquely determine a triangle?
Answer C: Two side lengths and an angle NOT between them
This condition (sometimes called the "ambiguous case") can produce 0, 1, or 2 different triangles, unlike the others, which uniquely determine a triangle.
Two sides of a triangle measure \(7\) cm and \(10\) cm. The angle between them is 60°. How many distinct triangles can be drawn?
Answer B: \(1\)
When two sides and the angle between them are given, exactly one triangle can be constructed (up to congruence).
A triangle has sides of length \(4\) cm, \(5\) cm, and \(6\) cm. Can you draw a different triangle with the same side lengths?
Answer C: No, exactly one shape (up to congruence)
When three specific side lengths are given, exactly one shape is determined (up to congruence). All triangles with sides \(4\), \(5\), \(6\) are congruent.
A rectangle is inscribed in a circle. One side is \(8\) cm and an adjacent side is \(6\) cm. Is there a unique rectangle that satisfies these conditions?
Answer A: Yes, exactly one
Given two adjacent sides of a rectangle (8 cm and 6 cm), the rectangle is completely determined. The circle's radius is half the diagonal length \(\sqrt{8^2+6^2}/2 = 5\) cm.
In triangle \(XYZ\), the angles are marked. How many distinct triangles can be drawn with these angles?
Answer C: Infinitely many
Knowing only the three angles determines the shape (similarity), not the size. Infinitely many triangles with angles \(40°, 60°, 80°\) exist at different scales.
A triangle has two angles of 45° and 65°. If one side is \(10\) cm, how many distinct triangles can be drawn?
Answer C: \(1\)
The third angle is \(180° - 45° - 65° = 70°\). When two angles and any side are given, the triangle is uniquely determined.
