Expressions, Equations, and Relationships>Extending Knowledge of Triangles to Angle Sums, Side Lengths, and Angle Measures(TEKS.Math.6.8.A)
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Texas 6th Grade Math › Expressions, Equations, and Relationships>Extending Knowledge of Triangles to Angle Sums, Side Lengths, and Angle Measures(TEKS.Math.6.8.A)
Can three segments with lengths 3 cm, 4 cm, and 8 cm form a triangle?
Yes, because the sums are all greater than the third side.
Yes, because 3 + 4 = 7.
No, because 8 is too small.
No, because 3 + 4 is not greater than 8.
Explanation
Triangle inequality: the sum of any two sides must be greater than the third. 3 + 4 = 7 is not greater than 8, so these lengths cannot form a triangle.
Triangle ABC has side lengths AB = 10 cm, BC = 6 cm, and AC = 8 cm. Which angle is the largest?
∠C
∠B
∠A
All angles are equal
Explanation
In a triangle, the longest side is opposite the largest angle. AB = 10 cm is the longest side, so the opposite angle ∠C is the largest.
A triangle has angles measuring 92° and 31°. What is the measure of the third angle?
59°
57°
61°
149°
Explanation
The angles in a triangle add to 180°. 92° + 31° = 123°. 180° − 123° = 57°.
In triangle XYZ, angle X = 40°, angle Y = 80°, and angle Z = 60°. Which side is the longest?
XZ
XY
YZ
All sides are equal
Explanation
In any triangle, larger angles are opposite longer sides. The largest angle is ∠Y = 80°, so the side opposite ∠Y is XZ, which is the longest.