Classifying Triangles by ANGLES

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Presentation transcript:

Classifying Triangles by ANGLES Geometry/Trig Name: _________________________ Introduction to Triangles Date: __________________________ ACUTE OBTUSE Classifying Triangles by ANGLES RIGHT EQUIANGULAR SCALENE ISOSCELSES EQUILATERAL Classifying Triangles by SIDES

Statements Reasons Statements Reasons Vertices of DABC: _________________ Sides of DABC: ___________________ Angles of DABC: ___________________ B A C Theorem: the three interior angles of a triangle sum to _________. x = ______ mÐA = _______ mÐB = _______ mÐC = _______ Example 1: mÐA = 56 mÐB = ____ mÐC = 82 Example 2: mÐA = 3x + 5 mÐB = x - 4 mÐC = 2x + 11 Given: ___________________________ Prove: ___________________________ Statements Reasons 1. 2. 3. 4. 5. 6. Corollary: The acute angles in a right triangle are ____________________. Given: ________________________ Prove: ________________________ Statements Reasons 1. 2. 3. 4. 5. 6.

Identify the remote interior angles for each exterior angle. Exterior Angle of a Triangle: An angle that forms a ____________________ with an interior angle of a triangle. In DABC, ____________, is an exterior angle. Remote Interior Angles: the two angles of the triangle that are not ____________ to a specific exterior angle. With respect to exterior Ð4, the remote interior angles are ___________ and _____________. Identify the remote interior angles for each exterior angle. Ð2 _______________ Ð6 ________________ Ð1 _______________ Ð5 ________________ Ð7 & Ð9 are remote interior angles for the exterior angles ________ Theorem: The exterior angle is equal to the sum of the two remote interior angles. Given: DABC Prove: mÐ1 + mÐ2 = mÐ4 Statements Reasons 1. 2. 3. 4. 5. Given: ________________________________ x = ____, mÐ1 = ____, mÐ2 = ____, mÐ3 = ____, mÐ4 = ____, mÐ5 = ____ Given: ________________________________ x = ____, mÐ1 = ____, mÐ2 = ____, mÐ3 = ____, mÐ4 = ____, mÐ5 = ____

A triangle with three congruent sides. Match the definitions with the correct vocab term. Then turn to page 93 and copy down the diagrams for each. A triangle one right angle (measures exactly 90 degrees). The other two angles are acute and are complementary. A triangle with three congruent sides. A triangle with three acute angles (all three angle measures are below 90 degrees). A triangle with NO congruent sides. A triangle with three congruent angles. The three angles all measure 60 degrees. These triangles are also classified as acute. A triangle with two congruent sides. A triangle with one obtuse angle (a angle that measures over 90 and under 180). The other two angles are acute.