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Geometry and Measurement 6-8 / Week 08 / Wednesday
3/6
Week 08 · Angles

Wednesday

Build Lab: The angles of a triangle
// Pairs that add up, pairs that match
⏱ about 20 min

Wednesday: Build Lab, The Angles of a Triangle

Rocket lays the four straw triangles from the roof frame on the Blueprint Table. "Measure every corner. Build Lab."

"Three angles each, twelve readings," Raven says. "Add each triangle's three angles. What do you notice?"

Rocket measures the peak truss. "60, 60, 60. That is 180." He measures the corner brace. "90, 45, 45. Also 180!"

"Every triangle?" Raven asks. "Even a long low one?"

Nova hovers over a paper triangle, her light on its three corners. "Tear the corners off," she says. "Lay them side by side."

Rocket tears and lays. The three corners fit together in a straight line. "180," he says. "A straight line, every time."

Your mission

Measure the three angles of four different triangles with a protractor and add them. Then tear the corners off a paper triangle and lay them along a line.

  • The crew's four roof-frame triangles, or four paper triangles cut with scissors. Make one wide, one tall, one with a square corner, one plain.
  • A protractor, a ruler and a pencil.
  • Your Blueprint Book for the table of readings.
Safety first
Cut paper with scissors only, sitting down, with a grown-up nearby.
Straws and the protractor stay on the table. No one runs with straws or sticks.
  1. Put the protractor's center on one corner of the triangle. Line up its zero line with one side.
  2. Read where the other side crosses the scale. Write the angle down.
  3. Repeat for the other two corners. Add the three angles.
  4. Do all four triangles. Compare the four sums.
  5. Tear the three corners off one paper triangle. Lay them point to point along a ruler's edge. What do they make?

The crew's lab table

These are the crew's own protractor readings from the roof frame, in degrees, written in Raven's Blueprint Book.

TriangleAngle 1Angle 2Angle 3Sum
peak truss60°60°60°180°
corner brace90°45°45°180°
side truss50°60°70°180°
low truss30°70°80°180°

Every sum is 180°. The torn corners show why: laid side by side, the three angles fill a straight line, and a straight line is 180°.

So two angles of a triangle are enough. Write a + b + ? = 180 and solve for the third.

A triangle with angles of 50° and 60° and its third angle marked with a question mark
READ THE LAB TABLE
  • Read the question.
  • Tap your answer.
A triangle with angles 50° and 60° and the third angle marked ?The side truss has angles of 50° and 60°. Without measuring, what is its third angle, in degrees?
A triangle with angles 30° and 70° and the third angle marked ?The low truss has angles of 30° and 70°. What is its third angle, in degrees?
A triangle with angles 90° and 45° and the third angle marked ?The corner brace has a square corner, 90°, and a 45° angle. What is its third angle, in degrees?
From the labTrue or false?
50 + 60 + 70 = 180?
A long, low triangle has a smaller angle sum than a tall one.?
Two angles of a triangle are enough to find the third.?
WHY THIS EXERCISEThe angle sum is a rule for every triangle, which is why the roof trusses can be checked without a third reading.
What do the three angles of every triangle add to, in degrees? Type the number.
WHY THIS EXERCISEThe angle sum of a triangle is the single most useful angle fact in the whole clubhouse.
Draw a triangle, then draw its three corners torn off and laid along a straight line. Label the line 180°.

Three corners, one straight line. Tomorrow the crew crosses two parallel sticks with a third and finds matching angles.

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