Thursday

Raven lays two sticks on the Blueprint Table, parallel, like two roof rafters. She lays a third stick across both. "The brace."

"Eight angles," Rocket says, counting. "Four at each crossing. Do I measure all eight?"

"Measure one," Raven says. "Angle a at the top is 70. What do you notice about the bottom crossing?"

Rocket slides the protractor down. "It looks exactly like the top one. Same four angles, just lower."

"Because the sticks are parallel, the brace meets them at the same slant," Raven says. "Same angles."

Nova hovers above the sticks, her light running along the brace. "Two kinds of angle on the whole figure," she says. "Find them both."

"Seventy and 110," Rocket says. "That is all." Nova hums. "Now the outside corner of the truss."

At the top crossing, angle a is 70°. Its vertical angle d matches it: 70°. Angles b and c sit along a straight line with a, so each is 180 - 70 = 110°.

The bottom crossing is a copy of the top one, slid down the transversal. The parallel lines meet it at the same slant.

So e matches a, h matches d, and f and g match b and c. Every angle on the figure is 70° or 110°.

The crew measured angle a on the Blueprint Table and worked out the rest. These are their own made-up measurements, in degrees.

Matching angles in the same spot at each crossing, like a and e, are called corresponding angles. They are equal: 70°.

Angles that make a straight line together, like a and b, are supplementary: 70 + 110 = 180.

Extend one side of the side truss past a corner. The angle outside, the exterior angle, sits along a straight line with the inside angle at that corner.

The inside angle is 180 - 50 - 60 = 70°. The exterior angle is 180 - 70 = 110°. That equals 50 + 60: the two far angles added.

Eight angles, two sizes. Tomorrow you find angle pairs around the house and review the week.