Grade 10 — Mathematics 10-3 › T3U05 The Pythagorean Theorem

Grade 10 › T3U05 The Pythagorean Theorem › L3
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-G2

L3 · Pythagoras on the job: clinic

Learning goal

“I can use the theorem the way it is used at work: the 3:4:5 layout check for square corners, diagonals of rectangular sheets and frames, ladder and guy-wire problems - in any orientation - and I can judge whether an answer is reasonable.”

Diagonal — the straight line across a rectangle from one corner to the opposite corner; it is the hypotenuse of the right triangle formed by two sides of the rectangle.
Square corner — job-site language for a true 90 degree corner; "the frame is in square" means its corners are right angles.
Brace — a diagonal board or strap fitted across a frame; its length is found with the theorem.
Guy wire — a cable anchored to the ground that holds a pole or tower upright; pole, ground and wire form a right triangle when the pole is plumb.
Worked example

A framer squares a wall corner. She measures 90 cm along one plate and 120 cm along the other, then measures between the marks. Step 1 (recognize the family): 90-120-? is 3:4:5 scaled by 30 - IF the corner is square, the diagonal must be 5 x 30 = 150 cm. Step 2 (use the reading): her tape reads 150 cm exactly. The corner is square. Step 3 (if it doesn't read 150): the corner is not square - nudge the longer side until it does. A reading of 148 cm means the angle is slightly less than 90 degrees; 152 cm means slightly more. Say it plainly: any multiple of 3:4:5 works - 30-40-50 on a small frame, 90-120-150 on a wall, 3 m-4 m-5 m on a foundation. The same check proves a PARALLELOGRAM is a rectangle: mark 3 and 4 along adjacent sides of the frame; if the diagonal between the marks is 5, that corner is 90 degrees, and a parallelogram with one right angle is a rectangle.

Check yourself — explain it

A checker marks 60 cm and 80 cm and the diagonal reads 103 cm. The corner is...

Paired problem — example still visible

Marks at 45 cm and 60 cm. What diagonal proves the corner is square? -> 75 cm (45-60-75 is 3:4:5 x 15; check: 2025 + 3600 = 5625 = 75^2)

Faded completion — last step is yours

"A foundation crew marks 6 m and 8 m. For a square corner the diagonal must read ___ m." -> 10 m

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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