Wednesday
Wednesday: Shop Lab, Triangle Braces
Comet fans out four cardboard triangles on the bench. "Brace shapes for the back of the flats. Lab day."
"Measure every angle first," Wren says, handing her the protractor. "Then we tear."
Comet measures brace 1. "Forty, seventy, and seventy." She tears the three corners off and lays them edge to edge. "A straight line."
"Every time?" Wren asks. "What does the evidence say?"
Brace 2, brace 3, brace 4. Every set of torn corners makes a straight line.
Nova hovers over brace 2 and projects a fold line down its middle. "Would you like a hint? Fold this one."
Comet folds. The two base angles land exactly on each other. "Equal sides, equal base angles. Our designer, run the lab with us."
What you need
- Four cardboard triangles, one with two equal sides, cut by a grown-up with scissors from a cereal box.
- A protractor, a ruler or tape measure, a pencil and a carpenter's square or any square corner.
- Your Shop Book and a sheet of paper for the torn corners.
Keep the bench clear and the scraps in one pile so nobody slips on cardboard.
Nothing heavy is lifted alone, and no one stands on the sawhorses.
Run the lab
- Measure the three angles of each triangle and write them in a table. Add them up.
- Tear off the three corners of one triangle. Lay them with their points touching along a straight edge.
- For the triangle with two equal sides, fold it so the equal sides meet. Do the base angles match?
- On a fresh triangle, mark the midpoint of two sides with the ruler. Join the midpoints with a pencil line.
- Measure the midsegment and the third side. Check with the square corner that the two are parallel.
These are the crew's own protractor readings for their four braces, in degrees.
| Brace | Angle A | Angle B | Angle C | Sum |
|---|---|---|---|---|
| Brace 1 | 40° | 70° | 70° | 180° |
| Brace 2 | 55° | 55° | 70° | 180° |
| Brace 3 | 90° | 35° | 55° | 180° |
| Brace 4 | 20° | 120° | 40° | 180° |
Why the corners always make a straight line
- Given: triangle ABC. Draw the line through C parallel to AB.
- The line makes two new angles at C, one on each side of angle C. The three angles at C make a straight line: 180°.
- AC is a transversal across the parallel lines, so the new angle on the A side equals angle A (alternate interior).
- BC is a transversal too, so the new angle on the B side equals angle B.
- So angle A + angle C + angle B = 180°. The angles of any triangle add to 180°.
Isosceles braces and midsegments
Brace 2 has two equal sides. Reflect it over the line that bisects the angle between them: the equal sides swap, so the base angles swap. They are congruent.
The midsegment of each brace measured half its third side and ran parallel to it. The crew's readings: third sides 60, 48, 90, 34 cm gave midsegments 30, 24, 45, 17 cm.
- Read the question.
- Tap your answer.
Brace 1 has angles of 40° and 70°. What is its third angle?
Brace 3 has a right angle and a 35° angle. What is its third angle?
Brace 4 has angles of 20° and 120°. What is its third angle?- Read the question.
- Tap your answer.
An isosceles brace has a 40° angle between its equal sides. What is each base angle?
Another isosceles brace has a 100° apex angle. What is each base angle?
A third has a 36° apex angle. What is each base angle?Fine lab work, designer. Tomorrow is Proof Day: the frame on the sawhorses finally earns its name.