Questions and Answers
What type of triangle has no congruent sides?
What type of triangle has two congruent sides?
What type of triangle has three congruent sides?
What type of triangle has three angles smaller than 90°?
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What type of triangle has one angle greater than 90°?
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What type of triangle has one angle equal to 90°?
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What type of triangle has three congruent angles?
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What is the angle and side classification of a Right-Scalene triangle?
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What is the angle and side classification of an Acute-Scalene triangle?
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What is the angle and side classification of an Obtuse-Scalene triangle?
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What is the angle and side classification of a Right-Isosceles triangle?
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What is the angle and side classification of an Acute-Isosceles triangle?
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What is the angle and side classification of an Obtuse-Isosceles triangle?
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What is the angle and side classification of an Equiangular-Equilateral triangle?
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Triangle DEF has one right angle. The other two angles must add up to equal ____________.
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Triangle ABC has three equal angles. What is the measurement of each angle?
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All angles in a triangle add up to equal ___________.
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The side length opposite the largest angle is going to be the ____________ of the three sides.
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The side length opposite the smallest angle is going to be the ____________ of the three sides.
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Triangle EFG could have side lengths of 10, 8, and ____.
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Triangle TUV could have side lengths of 12, 16, and ____.
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Any ________ side lengths of a triangle have a sum that is greater than the third side.
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Triangle XYZ has two angles that measure 68 and 50 degrees. The measurement of the third angle is ______.
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Triangle PQR has two angles that measure 120 and 32 degrees. The measurement of the third angle is _______.
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The first two angles in triangle JKL are equal. The third angle measures 98 degrees. The first two angles both measure _______.
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The midsize angle in a triangle will always be opposite the _______________ side length.
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The first angle in triangle CDE measures 82 degrees. The other two angles must add up to measure ___________ degrees.
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Study Notes
Types of Triangles by Sides
- Scalene Triangle: No sides are congruent; all sides have different lengths.
- Isosceles Triangle: Two sides are congruent; has at least two equal lengths.
- Equilateral Triangle: Three sides are congruent; all sides are equal in length.
Types of Triangles by Angles
- Acute Triangle: All three angles are less than 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees.
- Equiangular Triangle: All three angles are congruent; each angle measures 60 degrees.
Combination Classifications
- Right-Scalene: A right triangle with no equal sides.
- Acute-Scalene: An acute triangle with no equal sides.
- Obtuse-Scalene: An obtuse triangle with no equal sides.
- Right-Isosceles: A right triangle with two equal sides.
- Acute-Isosceles: An acute triangle with two equal sides.
- Obtuse-Isosceles: An obtuse triangle with two equal sides.
- Equiangular-Equilateral: An equilateral triangle, which is also equiangular.
Triangle Angle Measurements
- A right triangle has one angle equal to 90 degrees, while the other two angles must add up to 90 degrees.
- In an equiangular triangle, each angle measures 60 degrees.
- The sum of all angles in any triangle equals 180 degrees.
Side Length Relationships
- The longest side is opposite the largest angle and the shortest side is opposite the smallest angle.
- For a triangle with side lengths of 10, 8, and an unknown length, the third side must be less than 18 and greater than 2 (triangle inequality).
- In a triangle, the sum of any two side lengths must be greater than the length of the third side.
Angle Measurements in Specific Cases
- In Triangle XYZ, if two angles measure 68 and 50 degrees, the third angle measures 62 degrees (180 - 68 - 50).
- Triangle PQR with angles of 120 and 32 degrees results in the third angle measuring 28 degrees (180 - 120 - 32).
- If two angles are equal and the third measures 98 degrees in Triangle JKL, the first two angles each measure 41 degrees [(180 - 98) / 2].
Additional Insights
- The midsize angle in a triangle is opposite the mid-length side.
- The angles in a triangle determine relationships and constraints on the side lengths, forming the basis for triangle classifications.
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Description
Test your knowledge on different types of triangles with these flashcards. Learn about scalene, isosceles, equilateral, acute, and other triangle classifications based on their sides and angles. Perfect for geometry students and enthusiasts!
