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The sum of the measure of the angles of a triangle is 180o Corollary The acute angles of a right triangle are complementary. Exterior angle theorem An exterior angle of a triangle is equal in measure to the sum of the measures of its two remote interior angles. Triangle Proportionality Theorem
Two angles are complementary angles if they add up to _____ degrees. They do not have to be next to each other. When two lines intersect, four angles are created to having a point of intersection at the _____. The angles that are _____ from each other are considered to be vertical angles. They are also _____.
Definition In a protractor geometry {P, L, d, m}, we say ∠ABC is an acute angle if m(∠ABC) < 90, a right angle if m(∠ABC) = 90, and an obtuse angle if m(∠ABC) > 90. We say angles ∠ABC and ∠DEF are supplementary if. m(∠ABC) + m(∠DEF ) = 180. and we say angles ∠ABC and ∠DEF are complementary if. m(∠ABC) + m(∠DEF ) = 90.
EXAMPLE. 1 Identify Complements and Supplements. Determine whether the angles are complementary, supplementary, or neither. a. 228 b. c. 1588 158 858 558 358. Solution. Because 228 1 1588 5 1808, the angles are supplementary. Because 158 1 858 5 1008, the angles are neither complementary nor supplementary.
Examples: 1. Find the measure of the complement and supplement of a 43 angle. 2. ⊥Given: ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ , m 2 is three greater than twice m 1. Find the measure of each angle. 3. The measure of the supplement of an angle is 60 less than 3 times the measure of the complement of the angle.
The acute angles of a right triangle are complementary. The measure of each angle of an equiangular triangle is 600. = mZB = — 600 Theorem 4-2-4 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. mZ4 = mZ1 + mZ 3 4 The remote interior angles of L4 are Ll and 2
Congruent Triangles. If two triangles are congruent, then all of the parts of one triangle are congruent to the corresponding parts of the other triangle. This means that the corresponding sides and the corresponding angles are congruent.
