Classifying Triangles Worksheet - Practice identifying triangle types by angles and sides.

Let’s go through each problem step by step.

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Part 1: Classify each triangle as right, acute, or obtuse.

We know:
- A right triangle has one angle = 90°.
- An acute triangle has all angles < 90°.
- An obtuse triangle has one angle > 90°.

Also, remember: The sum of angles in any triangle is always 180°.

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Problem ①: Angles are 55°, 90°, and ?
→ One angle is 90° → Right triangle

Problem ②: Angles are 28°, 28°, and ?
→ Both given angles are less than 90°, but let’s find the third:
180 - 28 - 28 = 124° → 124° > 90° → Obtuse triangle

Problem ③: Angles are 30°, 100°, and ?
→ 100° > 90° → Obtuse triangle

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Part 2: Find the value of x (the measure of the third angle).

Again, use: Sum of angles = 180°

Problem ④: Angles are 120°, 20°, and x
→ x = 180 - 120 - 20 = 40°

Problem ⑤: Angles are 50°, 50°, and x
→ x = 180 - 50 - 50 = 80°

Problem ⑥: Right triangle → one angle is 90°, another is 45°
→ x = 180 - 90 - 45 = 45°

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Part 3: Classify each triangle as equilateral, isosceles, or scalene.

Definitions:
- Equilateral: All three sides equal.
- Isosceles: At least two sides equal.
- Scalene: All sides different.

Look at side markings — tick marks mean those sides are equal.

Problem ⑦: Sides labeled 12, 16, 7 → all different → Scalene

Problem ⑧: All three sides have same tick mark → all equal → Equilateral

Problem ⑨: Sides 8, 8, 10 → two sides equal → Isosceles

Problem ⑩: All three sides have same tick mark → all equal → Equilateral

Problem ⑪: Angles are 50°, 50°, so it’s isosceles (base angles equal) → sides opposite equal angles are equal → Isosceles

Problem ⑫: Angles are 70°, 45°, and ? → 180 - 70 - 45 = 65° → all angles different → all sides different → Scalene

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✔ Final Answers:

① Right
② Obtuse
③ Obtuse
④ 40°
⑤ 80°
⑥ 45°
⑦ Scalene
⑧ Equilateral
⑨ Isosceles
⑩ Equilateral
⑪ Isosceles
⑫ Scalene

Final Answer:
① Right, ② Obtuse, ③ Obtuse, ④ 40°, ⑤ 80°, ⑥ 45°, ⑦ Scalene, ⑧ Equilateral, ⑨ Isosceles, ⑩ Equilateral, ⑪ Isosceles, ⑫ Scalene