Questions and Answers
All equilateral triangles are isosceles.
True
All isosceles triangles are equilateral.
False
Triangles with no congruent sides are called skew.
False
Base angles of an isosceles triangle are not congruent.
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AAA is not a way to prove triangles congruent.
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SSA is always an acceptable method for proving triangles congruent.
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The vertex angle of an isosceles triangle can be congruent to the base.
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The remote interior angles of a triangle have a sum equal to the exterior angle.
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Congruent triangles sometimes—but not always—have the same shape and size.
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Obtuse triangles can have at most one obtuse angle.
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The non-right angles in an acute triangle are complementary.
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It is possible to have a right angle and an obtuse angle in the same triangle.
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An isosceles triangle may never be a right triangle.
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The congruent sides of an isosceles triangle are called legs.
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Study Notes
True or False Statements in Geometry
- All equilateral triangles are classified as isosceles due to having at least two equal sides.
- Not all isosceles triangles are equilateral, as an isosceles triangle can have two equal sides that are not the same length as the third side.
- A triangle with no congruent sides is termed scalene, not skew.
- In an isosceles triangle, the base angles are always congruent.
- AAA (Angle-Angle-Angle) does not prove triangle congruence, as it only shows similarity in shape.
- SSA (Side-Side-Angle) is not a reliable method for proving triangle congruence, leading to the possibility of ambiguous cases.
- The vertex angle of an isosceles triangle can indeed be congruent to one of the base angles in certain configurations.
- The sum of a triangle's remote interior angles equals its exterior angle.
- Congruent triangles must always have the same shape and size; this is a defining characteristic of congruence.
- Obtuse triangles can only contain one obtuse angle, as the angles in a triangle must sum to 180 degrees.
- In a right triangle, the two non-right angles are complementary, meaning they add up to 90 degrees.
- It is impossible to have both a right angle and an obtuse angle within the same triangle, as an obtuse angle exceeds 90 degrees.
- An isosceles triangle can indeed be a right triangle if the angles satisfy the properties of both classifications.
- The two equal sides of an isosceles triangle are referred to as legs.
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Description
Test your knowledge on key concepts in geometry with these true or false statements. Evaluate your understanding of triangles, including classifications and congruence properties. This quiz challenges your comprehension and application of geometric principles.
