Triangle Properties True or False

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Questions and Answers

A triangle is a polygon with exactly three vertices.

True

The word 'adjacent' refers to the segment across from an angle.

False

It is possible to have one angle in a triangle that is only 1°.

True

It is possible to have a triangle with more than one obtuse angle.

False Signup and view all the answers

If a triangle has a ratio of the angle measurements of 10:15:25, what is the measure of each angle?

36° : 54° : 90° Signup and view all the answers

Explain whether you can make a triangle with line segments measuring 10cm, 8cm, and 17cm.

Yes, you can make a triangle with these measurements. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Signup and view all the answers

Which is the correct equation for solving for side 'b'?

b = √(c² - a²) Signup and view all the answers

Is a triangle with side lengths 12cm, 16cm, and 20cm a right triangle?

No, it is not a right triangle. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagorean theorem), which doesn't hold true in this case. Signup and view all the answers

What is the minimum number of obtuse angles in a triangle?

Zero Signup and view all the answers

If two triangles have proportional corresponding side lengths, what can be said about their angles?

They are equal Signup and view all the answers

What is the maximum number of right angles in a triangle?

One Signup and view all the answers

What is the relationship between the side lengths of a triangle if the ratio of the angle measurements is 3:4:5?

The side lengths are proportional Signup and view all the answers

What is the Pythagorean Theorem equation for solving for side 'c'?

c^2 = a^2 + b^2 Signup and view all the answers

If a triangle has side lengths 3cm, 4cm, and xcm, what is the range of possible values of x?

x > 5cm Signup and view all the answers

What is the condition for three line segments to form a triangle?

The sum of the lengths of any two sides is greater than the third side Signup and view all the answers

If a triangle has side lengths a, b, and c, what is the Pythagorean Theorem equation for solving for side 'a'?

a^2 = b^2 + c^2 Signup and view all the answers

Study Notes

Triangles Basics

A triangle is a polygon with exactly three vertices.

Angles in Triangles

The word "adjacent" refers to the segment across from an angle.
It is not possible to have one angle in a triangle that is only 1°.
It is not possible to have a triangle with more than one obtuse angle.

Finding Missing Angles

To find a missing angle, use the fact that the sum of angles in a triangle is 180°.

Ratio of Angle Measurements

If a triangle has a ratio of the angle measurements of 10:15:25, the measures of each angle can be found by dividing 180° by the sum of the ratio (10+15+25=50) and then multiplying each part of the ratio by the quotient.

Forming Triangles with Line Segments

To form a triangle with three line segments, the sum of the lengths of any two segments must be greater than the length of the third segment.

Pythagorean Theorem

The correct equation for solving for side "b" is: b² = a² - c² or b = √(a² - c²).
The Pythagorean Theorem can be used to find the missing side length of a right triangle.

Solving for Unknown Sides

To solve for an unknown side length, use the Pythagorean Theorem or other trigonometric methods.

Right Triangles

A triangle with side lengths 12cm, 16cm, and 20cm is a right triangle because it satisfies the Pythagorean Theorem.
To determine if a triangle is a right triangle, use the Pythagorean Theorem.