Questions and Answers
Which type of triangle has all sides not congruent?
What is the term for a triangle with two sides that are congruent?
What type of triangle has all three sides congruent?
What are the names of the angles in a triangle?
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What is the Triangle Sum Theorem?
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Define what a median of a triangle is.
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Which theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent?
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What is the definition of an obtuse angle?
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All corresponding parts of congruent triangles are congruent.
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The statement 'If two sides of a triangle are congruent, then the angles opposite those sides are congruent' is known as the _____ Theorem.
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Which function is not allowed in congruence?
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All radii of a circle are ___.
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What does C.P.C.T.C. stand for?
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Study Notes
Triangle Types by Sides
- Scalene Triangle: No sides are congruent.
- Isosceles Triangle: Two sides are congruent.
- Equilateral Triangle: All three sides are congruent.
Triangle Types by Angles
- Obtuse Triangle: Contains one angle greater than 90°.
- Right Triangle: Contains one angle equal to 90°.
- Acute Triangle: All three angles are less than 90°.
- Equiangular Triangle: All three angles are exactly 60°.
Classifying Triangles
- Measure distances of all sides using the distance formula.
- Keep distances in square root format for accuracy.
- Classify as:
- Scalene: All sides different.
- Isosceles: Two sides the same.
- Equilateral: All three sides the same.
- Use the Pythagorean theorem for right triangle classification:
- Right Triangle: ( leg^2 + leg^2 = hypotenuse^2 )
- Acute Triangle: ( leg^2 + leg^2 > hypotenuse^2 )
- Obtuse Triangle: ( leg^2 + leg^2 < hypotenuse^2 )
Key Triangle Theorems
- Triangle Sum Theorem: The interior angles of a triangle sum to 180°.
- Exterior Angles Theorem: An exterior angle equals the sum of two non-adjacent interior angles.
- Third Angles Theorem: If two triangles have two congruent angles, the third angles are also congruent.
Triangle Congruence Criteria
- S.A.S. (Side-Angle-Side): Two sides and included angle are congruent.
- S.S.S. (Side-Side-Side): All three sides are congruent.
- Hypotenuse-Leg: Hypotenuse and one leg are congruent in right triangles.
- A.S.A. (Angle-Side-Angle): Two angles and included side are congruent.
- A.A.S. (Angle-Angle-Side): Two angles and a non-included side are congruent.
Non-allowed Congruence Functions
- A.S.S. and S.S.A. configurations are not valid for proving triangle congruence.
Angle Types Within Triangles
- Base Angles: Angles connected to both a leg and the base of the triangle.
- Vertex Angle: Angle formed by the two legs of the triangle.
Base Angles Theorem and Converse
- Base Angles Theorem: If two sides are congruent, then the angles opposite those sides (base angles) are also congruent.
- Base Angles Theorem Converse: If the two base angles are congruent, then the sides opposite those angles are congruent.
Congruence of Polygons
- If all corresponding parts (sides and angles) of polygons are congruent, then the polygons themselves are congruent.
Medians and Altitudes of Triangles
- Median: Segment from a vertex to the midpoint of the opposite side.
- Altitude: Segment from a vertex to the opposite side, forming right angles with that side.
Auxiliary Lines
- Lines, rays, or segments not in the original triangle figure, added for geometric proof or analysis.
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Description
Test your understanding of triangle properties with this quiz based on Chapter 5 of the Big Ideas Math curriculum. Focus on the names and classifications of triangle sides and angles, including scalene, isosceles, equilateral, obtuse, right, and acute triangles.
