7th Grade Drawing Triangles from Given Conditions Worksheet Solutions (PDF)
This triangle constructions 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 to check your work on the drawing triangles worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.
Grade 7 · Common Core State Standards: 7.G.A.2
Triangle constructions answers: exercises 1 to 10
Exercise 1 – Check 3, 4, 5
\(3+4=7>5\).
Yes
Exercise 2 – Check 2, 3, 7
\(2+3=5\), which is less than 7.
No
Exercise 3 – Exactly equal
\(5+5=10\), which is not greater than 10. The sides lie flat.
No
Exercise 4 – A right triangle?
\(6+8=14>10\), \(6+10=16>8\), \(8+10=18>6\).
All three sums work
Exercise 5 – Angles that fit
\(50+60+70=180\), so they fit.
Any enlarged or reduced copy has the same angles, so the triangle is not unique.
Yes; many triangles
Exercise 6 – Angles that don't fit
\(90+60+40=190\ne 180\).
No
Exercise 7 – How many triangles?
\(4+6=10>7\), so a triangle exists.
Three fitting side lengths give exactly one shape.
Exactly one
Exercise 8 – Third angle
\(180-40-60=80\)
\(80^{\circ}\)
Exercise 9 – Range of the third side
The third side must be less than \(5+8=13\) and greater than \(8-5=3\).
Between 3 in and 13 in (not including 3 or 13)
Exercise 10 – Included angle
The triangle is isosceles, so the two base angles are equal: \((180-60)\div 2=60\).
All angles are \(60^{\circ}\), so it is equilateral with all sides 4 in.
Angles \(60^{\circ}\), \(60^{\circ}\); third side 4 in
Exercises 11 and up
Exercise 11 – Unique or not?
Two angles and the side between them fix the triangle, so it is unique.
\(180-35-65=80\)
Unique; \(80^{\circ}\)
Exercise 12 – Isosceles perimeter
\((20-8)\div 2=6\).
Check: \(6+6=12>8\).
6 in
Exercise 13 – Describe the drawing
1. Draw a 5-inch base.
2. With the compass at one end, draw an arc of radius 4 in; at the other end, an arc of radius 3 in.
3. Join the point where the arcs meet to both ends of the base.
One triangle (right angle opposite the 5-inch side)
Exercise 14 – Right isosceles
The angles add to 180, but triangles of different sizes share them.
Giving one side length, such as a leg of 4 in, makes it unique.
Not unique; give one side
Exercise 15 – Craft sticks
\(7+3=10\), which equals the longest stick.
No, the sticks lie flat
Exercise 16 – Whole-number third side
The third side is greater than \(9-6=3\) and less than \(6+9=15\).
Whole numbers: 4, 5, …, 14, which is \(14-4+1=11\) values.
11 lengths
Exercise 17 – Three towns
\(5+8=13>12\).
Yes
Exercise 18 – Roof truss
\(180-35-35=110\)
\(110^{\circ}\)
Exercise 19 – Perimeter 30
\(30-9-12=9\).
Check: \(9+9=18>12\).
9 in
Exercise 20 – Tent base
The base must be greater than \(0\) and less than \(5+5=10\).
9 lengths (1 through 9 ft)
Key facts behind this triangle constructions answers
- 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 answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the triangle constructions answers as a PDF with the button below and keep it with your notes.
All Grade 7 chapters: Grade 7 math.
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