7.G.2: Draw Triangles from Given Conditions
Also written as 7.G.A.2 and CCSS.MATH.CONTENT.7.G.A.2 · Cluster: Draw construct, and describe geometrical figures and describe the relationships between them.
The Official Wording
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Common Core State Standards, Grade 7, Geometry · Read it at the source · Checked October 14, 2026
What 7.G.2 Means in Plain English
Seventh graders draw triangles from given measures with a ruler, protractor, compass or geometry app, and notice what the measures allow. Sides of 5, 6 and 9 cm make exactly one triangle; sides of 3, 4 and 8 cm make none, because 3 + 4 falls short of 8.
Angles alone, like 40°, 60° and 80°, make endless triangles of one shape in different sizes. That noticing feeds the 8th-grade argument for the triangle angle sum (8.G.5) and, in high school, the SSS, SAS and ASA congruence criteria (HSG-CO.8).
7.G.2 I Can Statements
- I can draw a triangle from given side lengths or angles.
- I can tell when three side lengths cannot make a triangle.
- I can decide whether conditions give one triangle, many, or none.
7.G.2 Worked Example
Four sets of measures, four drawings attempted, and three different verdicts: one triangle, many triangles, or none at all.
Try to draw each triangle. Which conditions give exactly one triangle, more than one, or none? (a) sides 3 cm, 4 cm, 8 cm (b) sides 5 cm, 6 cm, 9 cm (c) angles 40°, 60°, 80° (d) angles 50°, 60°, 80°
- (a) Lay the 8 cm side down and swing the 3 cm and 4 cm sides up from its ends. Together they reach only 7 cm, so they can never meet.3 + 4 = 7, less than 8: no triangle
- (b) The two short sides reach past the long one, so the triangle closes. With a compass, arcs of 5 cm and 6 cm from the ends of the 9 cm base cross at one point.5 + 6 = 11, more than 9: exactly one triangle
- (c) The angles add to 180°, so the triangle exists, but no side is given. Draw it on a 4 cm base and again on an 8 cm base: same angles, different sizes.40 + 60 + 80 = 180: many triangles, one shape
- (d) Add the angles before drawing. Every triangle’s angles total exactly 180°.50 + 60 + 80 = 190: no triangle
Check it: Cut out every student’s triangle for (b) and stack them: they match exactly. Stack the triangles for (c) and the angles line up, but the sides do not.
Common Mistakes with 7.G.2
Checking the wrong pair of sides
Sides 3, 4 and 8: 3 + 8 is more than 4, so it works
Try this: Add the two shortest sides and compare with the longest; if 3 + 4 is not more than 8, the triangle cannot close.
Thinking three angles fix the triangle
40°, 60° and 80° make one triangle, so every drawing will match
Try this: Draw it on a 4 cm base, then an 8 cm base: same angles, different sizes, so angles alone allow many triangles.
Drawing before adding the angles
50° and 60° drawn on a base, the sides joined, and the third angle labeled 80°
Try this: Add all three angles before picking up a protractor; a total other than 180° means no triangle, and the drawn third angle measures 70°.
Where 7.G.2 Fits
Practice 7.G.2
Quick Check
- Can sides of 6 cm, 7 cm and 14 cm make a triangle?
- Can a triangle have angles of 35°, 55° and 90°? How many such triangles are there?
- A triangle has sides of 5 cm and 7 cm with a 60° angle between them. One triangle, many, or none?