7th Grade Drawing Triangles from Given Conditions Test Solutions and Scoring (PDF)

7th Grade math test solutions: Drawing Triangles from Given Conditions – Maths PDF

Cover of the book Grade 7 Math Tests with Answer Keys (PDF)

Download as a PDFThe Grade 7 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This triangle constructions test answers for 7th Grade covers drawing triangles from given conditions (Common Core 7.G.A.2), with a free PDF to print.

Use this answer key and scoring guide to grade the drawing triangles test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

Grade 7 · Common Core State Standards: 7.G.A.2

Triangle constructions test answers: worked solutions

Question 1 – Triangle inequality [2 pts]

A: \(4+5=9>8\) yes.

B: \(3+4=7< 8\) no.

C: \(6+6=12\) not greater than 12, so no.

Only set A

Scoring: 1 point for two correct decisions with checks; 1 point for all three.

Question 2 – Angle sum [2 pts]

\(72+68+40=180\), yes.

\(180-55-75=50\)

Yes; \(50^{\circ}\)

Scoring: 1 point for each part.

Question 3 – How many triangles? [2 pts]

Exactly one: \(5+6=11>7\).
More than one: no side is given.
None: \(3+3=6< 9\).

(a) one, (b) many, (c) none

Scoring: Half credit for two correct parts; full credit for three with reasons (round up).

Question 4 – Perimeter and range [2 pts]

Perimeter: \(4+5+7=16\) in.

Third side: greater than \(5-4=1\) and less than \(4+5=9\).

16 in; between 1 in and 9 in

Scoring: 1 point for the perimeter; 1 point for the range.

Question 5 – Included angle [2 pts]

Draw the 7 cm side as a base. Use a protractor to draw \(40^{\circ}\) at one end. Mark 5 cm along the new ray and join the endpoints.

Two sides and the included angle give exactly one triangle.

Unique

Scoring: 1 point for the steps; 1 point for uniqueness.

Question 6 – Isosceles angles [2 pts]

\(180-50-50=80\).

Many triangles of different sizes share these angles.

\(80^{\circ}\); not unique

Scoring: 1 point for the angle; 1 point for the uniqueness reason.

Question 7 – Whole-number sides [2 pts]

Greater than \(11-8=3\) and less than \(8+11=19\): the values 4 through 18.

\(18-4+1=15\)

Scoring: 1 point for the range; 1 point for the count.

Question 8 – Stick kit [3 pts]

\(4+6=10>9\), so yes.
\(2+6=8< 9\), so no.
The stick must be longer than \(9-6=3\), so 4 in.

With a 2-inch stick, the sum 8 is less than 9.

Scoring: 1 point for each part.

Question 9 – Kite frame [3 pts]

\(10+10=20>15\), so yes.
\(10+10+15=35\) in.
\(10+10=20\) is not greater than 20, so no triangle.

10 + 10 = 20 gives a flat line.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this triangle constructions test answers

Key facts

Triangle inequality: the sum of any two sides is greater than the third side.
The angles of a triangle add up to \(180^{\circ}\).
Three fitting side lengths determine exactly one triangle.
Three angles alone give many triangles of different sizes.
Two sides and the angle between them determine exactly one triangle.

How to use this triangle constructions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 7 chapters: Grade 7 math.

Voter.. post

Free printable PDF