Construct Shapes

Videos, examples, solutions, and lessons to help Grade 7 students learn how to 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: 7.G.2

Suggested Learning Targets

• I can construct geometric shapes using appropriate tools (freehand, ruler, protractor, or technology).
• I can describe the attributes of geometric figures (with focus on triangles).
• I can construct triangles with given angle and side conditions.
• I can explain with given measures, why they form a unique triangle, more than one triangle, or no triangle.

7.G.2 Triangles
Examples:

1. Classify each triangle.
a. The triangle has one obtuse angle and no congruent sides.
b. The triangle has all acute angles and two congruent sides.
2. Draw a triangle with angle measures of 30°, 60°, and 90°. Then classify the triangle.
Step 1: Use a protractor to draw a 30° angle.
Step 2: Use a protractor to draw a 60° angle.
Step 3: The protractor shows the measure of the remaining angle is 90°.
3. Draw a triangle with a 3-centimeter side and a 4-centimeter side that meet at a 30° angle. Then classify the triangle.
4. Draw a triangle with angle measures of 45°, 45°, and 90°. Then classify the triangle.
5. Draw a triangle with a 1-inch side and a 2-inch side that meet at a 60° angle. The classify the triangle.

Drawing Triangles 1 (7.G.2)
Rule: A triangle’s angles must sum to 180 degrees.
Which of the following is possible to draw as a triangle?
32° 53° 95°
40° 30° 120°

How many triangles can you draw?
30° 60° 90°
60° 60° 60°

Drawing a Triangle
This lesson demonstrates how to draw a triangle using a protractor and a measure.
Example:

1. Draw a triangle with a 100 degree angle between two 2 inch sides.
2. Draw a triangle with a 5cm side between a 70 degree angle and a 50 degree angle.

How to draw a triangle when you are told the lengths of one side and you have two angles?
Example:
Draw a triangle ABC with AB = 7cm, angle BAC = 40° and angle ABC = 65°

Drawing Triangles
Example:
Use a ruler and a protractor to draw triangle RPQ.

Constructing Triangles from the measure of Sides and Angles

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.