Grade 10 — Mathematics 10-3 › T3U06 Similarity of Polygons

Grade 10 › T3U06 Similarity of Polygons › L1
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-G3

L1 · Similar convex polygons: corresponding sides and angles

Learning goal

“I can decide whether two convex polygons are similar by checking BOTH conditions - corresponding angles equal AND corresponding sides in one common ratio - and I can explain, with a counterexample, why one condition alone is not enough.”

Similar polygons — same shape, possibly different size: corresponding angles are equal and corresponding sides are all in the same ratio.
Corresponding — matching parts in the same relative position: the side between the two largest angles in one polygon corresponds to the side between the two largest angles in the other.
Scale factor — the single multiplier that takes every side of one polygon to the corresponding side of the other (e.g., scale factor 2 doubles every side).
Convex polygon — a polygon with no dents: every interior angle is less than 180 degrees. (This course studies convex polygons only.)
Worked example

Rectangle P is 4 cm by 6 cm. Rectangle Q is 6 cm by 9 cm. Are they similar? Step 1 (ANGLE list): every angle in both rectangles is 90 degrees. Angles match - condition 1 passes. Step 2 (RATIO table): match corresponding sides (short with short, long with long): 4/6 = 0.667 and 6/9 = 0.667. One common ratio: 2/3. Condition 2 passes. Step 3 (verdict): BOTH conditions pass - P and Q are similar. The scale factor from P to Q is 3/2 (each side multiplied by 1.5): 4 x 1.5 = 6, 6 x 1.5 = 9. Say it plainly: angles tell you the corners match; the ratio table tells you the shape was stretched EVENLY. Similar means same shape - corners matching AND even stretching (when the angles are equal, the corresponding sides carry the shape's proportions, and ALL of those ratios must agree).

Check yourself — explain it

A square and a rectangle both have four 90 degree angles. They are...

Paired problem — example still visible

Triangles: T1 has angles 40°, 60°, 80°. T2 has angles 40°, 60°, 80° and sides exactly double T1's. Similar? -> Yes - angles equal, and every side ratio is 1/2 (scale factor 2).

Faded completion — last step is yours

"Rectangles 5 cm x 10 cm and 10 cm x 20 cm: ratios are 5/10 = ___ and 10/20 = ___. Both equal ___, so the rectangles are ___." -> 0.5; 0.5; 0.5; similar

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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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