A focused Grade 7 learning session for Constructing Triangles from Three Measurements using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving constructing triangles from three measurements.
Constructing Triangles from Three Measurements 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 constructing triangles from three measurements 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 Constructing Triangles from Three Measurements, 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 constructing triangles from three measurements.
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 unique triangles can be constructed with sides of length \(6\) cm, \(8\) cm, and \(10\) cm?
Answer B: \(1\)
Given three specific side lengths that satisfy the Triangle Inequality, exactly one unique triangle (up to congruence) can be formed. In fact, this is a right triangle because \(6^2+8^2=10^2\).
Which set of side lengths will NOT form a triangle?
Answer B: \(4\) cm, \(6\) cm, \(9\) cm
The Triangle Inequality states the sum of any two sides must exceed the third. Check: \(4+6=10\) is not greater than \(9\), so this fails.
Triangle \(ABC\) with \(AB=5\) cm, \(AC=4\) cm, and a right angle at \(A\) satisfies which congruence condition?
Answer B: SAS
Two sides and the included right angle are given: \(AC=4\) cm, \(AB=5\) cm, and angle \(A=90°\) is between them. This is SAS (Side\textendash{}Angle\textendash{}Side) congruence.
Two triangles each have angles measuring 50°, 60°, and 70°. Are the triangles congruent?
Answer D: Cannot be determined without side lengths
AAA (Angle\textendash{}Angle\textendash{}Angle) guarantees similarity, not congruence. The triangles could be different sizes but the same shape. At least one side length is needed to prove congruence.
Triangle \(DEF\) has sides \(DE=7\) cm, \(EF=6\) cm, and \(FD=8\) cm. Is this triangle unique?
Answer B: Yes, SSS guarantees uniqueness
When all three side lengths are specified (7 cm, 6 cm, 8 cm), exactly one unique triangle (up to congruence) can be constructed. This is the SSS (Side\textendash{}Side\textendash{}Side) condition.
A triangle has sides of length \(5\) m and \(9\) m. Which length CANNOT be the third side?
Answer D: \(15\) m
The Triangle Inequality requires the sum of any two sides to exceed the third. With sides 5 and 9: we need \(5+9>c\), so \(c<14\) m. Also \(5+c>9\), so \(c>4\) m. Thus \(4
If \(GH=7\) cm and angles \(\alpha\) and \(\beta\) at \(G\) and \(H\) are known, which congruence condition applies?
Answer B: ASA
We have angle \(\alpha\) at \(G\), the side \(GH=7\) cm between them, and angle \(\beta\) at \(H\). This is Angle\textendash{}Side\textendash{}Angle (ASA): two angles and the included side are given.
Which statement best describes the SSA (Side\textendash{}Side\textendash{}Angle) condition for constructing triangles?
Answer B: SSA may produce zero, one, or two triangles
SSA is the ambiguous case. Depending on the side lengths and angle, there may be no valid triangle (Triangle Inequality violated), exactly one triangle (right angle or obtuse), or two distinct triangles (acute angle with proper side ratio).
Triangle \(JKL\) has base \(JK=8\) cm and perpendicular height \(h=3\) cm. How many distinct triangles satisfy these conditions?
Answer C: Infinitely many
The vertex \(L\) may lie anywhere on a line parallel to \(JK\) at distance 3 cm above it. Each position yields a different triangle with the same base and height but different side lengths and angles.
A triangle has two sides of length \(5\) cm and \(7\) cm, with an included angle of 45°. How many distinct triangles can be constructed with these measurements?
Answer B: \(1\)
Two sides and the included angle uniquely determine a triangle by the SAS (Side\textendash{}Angle\textendash{}Side) condition. Exactly one triangle can be constructed.
Triangle \(MNO\) has sides \(MN=5\) cm, \(NO=4\) cm, and \(OM=5\) cm. What type of triangle is \(MNO\)?
Answer B: Isosceles
Two sides have the same length: \(OM=MN=5\) cm. An isosceles triangle has at least two congruent sides. Checking: \(4^2+5^2=41\neq 25\), so it is not a right triangle.
