Drawing Geometric Shapes: Constructing Triangles and Exploring Uniqueness

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Grade 7·21 problems·~35 min·Common Core Math - Grade 7·standard·7-g-a-2

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Recall / Warm-Up

Which type of angle has a measure of 115°?

Acute

Right

Obtuse

Straight

In triangle XYZ, angle X measures 72° and angle Y measures 41°. What is the measure of angle Z?

67°

113°

108°

139°

In triangle PQR, which angle is the included angle between sides PQ and PR?

Angle Q

Angle R

Angle P

There is no included angle between PQ and PR.

Which set of side lengths can form a valid triangle?

2, 5, 10

3, 6, 9

4, 6, 9

1, 3, 8

A student constructs a triangle with sides 5 cm, 8 cm, and 6 cm using SSS. How many distinct triangles can be made with these three side lengths?

Zero — this fails the triangle inequality.

Exactly one (up to congruence).

Exactly two — one triangle and its mirror reflection.

Infinitely many — the angles are not fixed.

Which condition always produces exactly one distinct triangle (up to congruence)?

Three angle measures (AAA)

Two sides and the included angle (SAS)

Two sides and a non-included angle (SSA)

Three angles that sum to 180°

In triangle DEF, angle D measures 55° and angle E measures 48°. What is the measure of angle F, in degrees?

You draw a triangle with angles 40°, 60°, and 80°. How many different triangles exist with these same three angle measures?

Exactly one — three conditions always determine a unique triangle.

None — you need at least one side length to construct any triangle.

Infinitely many — the angles fix the shape but not the size.

Exactly two — one for each orientation.

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