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Triangles

Definitions

triangle: A three-sided polygon. Triangles have three angles and three vertices.

Naming Triangles

Name the red triangle.

Step 1: Triangles are named by listing the vertices in any order. The vertices of the red triangle are E, F and G. The symbol for triangle is a small triangle, ∆.

The red triangle is ∆ EFG.

Test-Taking Hint

Word problems, or story problems, should be answered in complete sentences.

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TEST TIME: Show Your Work

Sean has three pipe cleaners. The lengths are 8 inches, 5 inches, and 4 inches. Can Sean make a triangle from the three pipe cleaners?

For any three lengths to form a triangle, the sum of the shorter two lengths must be greater than the longest length. Add the two shortest lengths and compare the sum to the longest.

Solution:

The two shortest pipe cleaners are 5 inches and 4 inches.
5 inches + 4 inches = 9 inches

The longest pipe cleaner is 8 inches.
Is 9 inches greater than 8 inches? Yes.

Yes, Sean can make a triangle using the three pipe cleaners.

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Definitions

acute triangle: A triangle with three angles less than 90°.

right triangle: A triangle with one 90° angle.

obtuse triangle: A triangle with one angle greater than 90°.

equilateral triangle: A triangle with three congruent sides. Equilateral triangles are also equiangular. They have three congruent angles.

isosceles triangle: A triangle with exactly two congruent sides.

scalene triangle: A triangle with no congruent sides.

Test-Taking Hint

Small hatch marks and arcs are used to show that sides or angles are congruent.

Test-Taking Hint

Knowing the names of angles (acute, right, and obtuse) will help you remember the names of triangles.

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TEST TIME: Multiple Choice

Classify ∆ ABC by angle measure and by side length.

Look at the angles of triangle ABC. Angles B and C are acute. Angle A is obtuse. Triangle ABC is obtuse.

Look at the sides of triangle ABC. Two sides have the same length. They are congruent. Triangle ABC is isosceles.

Solution: Answer d is correct.

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