Unit 2: "Triangle Congruence & Relationships" for Quiz 1 Exam with verified solutions 2024

Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180 Auxiliary Line Line helping to prove that a triangle's angles add up to 180 using AIA's, angles that form a straight line, substitution Corollary A statement that can be easily proved by applying a theorem - extension of a theorem & can be used as reasons in proof 4.1 The acute angles of a right triangle are complementary. 4.2 There can be at most one right or obtuse angle in a triangle Segments Sides of a triangle Vertex The interior angles of the triangles - no using the measures Scalene Triangle No sides are congruent Isosceles Triangle AT LEAST 2 sides are congruent Base Angles The congruent angles of an isosceles angle Vertex Angle The non-congruent angle of an isosceles triangle Equilateral Triangle All sides are congruent Is an isosceles triangle and equilateral triangle too? Sometimes Is an equilateral triangle an isosceles triangle too? Always Triangle can be classified by its ANGLES & # of CONGRUENT sides Acute Triangle Three acute angles Obtuse Triangle One obtuse angle Right Triangle One right angle Hypotenuse Longest side of a right angle, opposite of the right angle Legs The two shorter sides of a right angle Equiangular Triangle All angles are congruent Does an equiangular triangle have to be equilateral? Always Does an equilateral triangle have to be equiangular? Always Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles Remote Interior Angles The angles that add up to the exterior angle - not adjacent Exterior Angle When one side of a triangle is extended, an EXTERIOR ANGLE is formed If a triangle is scalene, then it is ___ isosceles Never If a triangle is obtuse, then it is ___ isosceles Sometimes Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the thrid angles of the triangles are congruent. CPCTC Corresponding Parts of Congruent Triangles are Congruent Does knowing all three congruent angles make two triangles congruent? No Does knowing all three side lengths make two triangles congruent? Yes SSS Congruence Side-Side-Side: If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. SAS Congruence Side-Angle-Side: If two sides and the included angle one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. Included Angle The angle that is