Geometry & Mensuration • Topic 2 of 5

Triangles & Congruence

A triangle's angles sum to 180; an exterior angle equals the sum of the two remote interior angles. Pythagoras holds in right triangles. Similar triangles have equal angles and proportional sides; if the side ratio is k, the area ratio is k^2. Standard centres: the centroid divides each median 2:1. Memorise common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) for instant answers.

✅ Solved examples

1. Two angles of a triangle are 50 and 60 degrees. The third?
180 - 110 = 70 degrees.
2. Right triangle legs 6 and 8. Hypotenuse?
root(36 + 64) = root 100 = 10.
3. Similar triangles have side ratio 2:3. Area ratio?
k^2 = 4:9.
4. Exterior angle of a triangle is 120, one remote interior is 50. The other remote?
120 - 50 = 70 degrees.

✏️ Practice — try these, take hints as needed

1. Angles 45 and 65. Third?
180 - 110.
—
—
70 degrees
2. Legs 9 and 12. Hypotenuse?
root(81+144).
root 225.
—
15
3. Side ratio 3:5 -> area ratio?
k^2.
9:25.
—
9:25
4. Hypotenuse 13, one leg 5. Other leg?
root(169-25).
root 144.
—
12
5. Centroid divides a median in ratio?
Vertex to centroid : centroid to midpoint.
—
—
2:1

📝 Topic test — 8 questions

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