Triangle Classification: Identifying a Shape with 70°, 70°, and 40° Angles

Q: What makes this triangle isosceles instead of just acute?

An isosceles triangle has two equal angles and two equal sides. Since this triangle has two 70° angles, it's isosceles. It's also acute (all angles isosceles is the more specific classification.

Q: How do I remember the difference between isosceles and equilateral?

Isosceles: 2 equal angles and 2 equal sidesEquilateral: 3 equal angles (60° each) and 3 equal sidesThink: iso = two same, equi = all same

Q: Can a triangle be both isosceles and acute?

Yes! This triangle is both isosceles and acute. Isosceles describes the equal angles/sides, while acute describes that all angles are less than 90°. They're different classification systems.

Q: What if I calculated the angles wrong?

Always double-check that your three angles add up to exactly 180°. If they don't, recheck your angle measurements or calculations. Every triangle must follow this rule!

Q: Why isn't this a right triangle?

A right triangle needs one 90° angle. This triangle's largest angle is only 70°, so all angles are acute (less than 90°). No right angle means it's not a right triangle.

Triangle Classification with Equal Base Angles

What kind of triangle is given in the drawing?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify what type of triangle is shown in the drawing

00:03 Let's check the triangle's angles and their relation to a right angle

00:06 Angle A is less than a right angle

00:11 The same applies to angles B and C

00:14 A triangle where all angles are less than 90 degrees is acute

00:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What kind of triangle is given in the drawing?

Step-by-step solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

$70+70+40=180$

The triangle is isosceles.

Final Answer

Isosceles triangle

Key Points to Remember

Essential concepts to master this topic

Angle Sum Rule: All triangle angles must sum to exactly 180°
Classification Technique: Two equal angles (70°, 70°) means isosceles triangle
Verification: Check angle sum: 70° + 70° + 40° = 180° ✓

Common Mistakes

Avoid these frequent errors

Classifying by largest angle only
Don't just look at the 70° angles and call it acute = missing the isosceles property! This ignores the key geometric relationship. Always check for equal angles first to identify isosceles triangles.

Practice Quiz

Test your knowledge with interactive questions

Is the triangle in the drawing a right triangle?

FAQ

Everything you need to know about this question

What makes this triangle isosceles instead of just acute?

An isosceles triangle has two equal angles and two equal sides. Since this triangle has two 70° angles, it's isosceles. It's also acute (all angles < 90°), but isosceles is the more specific classification.

How do I remember the difference between isosceles and equilateral?

Isosceles: 2 equal angles and 2 equal sides
Equilateral: 3 equal angles (60° each) and 3 equal sides
Think: iso = two same, equi = all same

Can a triangle be both isosceles and acute?

Yes! This triangle is both isosceles and acute. Isosceles describes the equal angles/sides, while acute describes that all angles are less than 90°. They're different classification systems.

What if I calculated the angles wrong?

Always double-check that your three angles add up to exactly 180°. If they don't, recheck your angle measurements or calculations. Every triangle must follow this rule!

Why isn't this a right triangle?

A right triangle needs one 90° angle. This triangle's largest angle is only 70°, so all angles are acute (less than 90°). No right angle means it's not a right triangle.

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