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TRIANGLES • Equilateral • Isosceles • Scalene Right Acute Obtuse TRIANGLES • Equilateral: A triangle with 3 congruent sides. Equilateral: A triangle with 3 congruent ANGLES. • Isosceles: A triangle with 2 congruent sides. • Scalene: A triangle with no congruent sides. TRIANGLES • Acute: A triangle with 3 acute angles. • Right: A triangle with one right angle. • Obtuse: A triangle with one obtuse angle. PARTS OF A TRIANGLE Every triangle is made up of three sides connected by vertexes. side vertex Triangle Sum Theorem: The sum of the measurements of each triangle add up to 180º. 60º 60º 50º xº X = 60º (60+60+60=180) 90º xº X=40º (90+50+40=180º) EXTERIOR AND INTERIOR ANGLES (TRIANGLE PARTS CONT.) • Exterior Angle: The angle formed outside the angle when an extension is drawn to the triangle. • Interior Angle: Any angle formed inside the triangle. EXTERIOR ANGLE THEOREM • We can use this theorem when we need to find an angle and an exterior angle is available. We can use this theorem when a triangle shape is used in a construction. • m<4 = m<1 + m<2 • Examples: 55º 45º x=85º 65º 50º xº yº y=60º 35º z=55º 90º zº CONGRUENCE IN SHAPES AND CTCP • A shape is congruent to the other if they have the same shape, size, and measure. • CPCT: Corresponding Parts of Congruent Triangles. • EXAMPLES: A w 3 cm. 6 cm. B x CD=3 cm. D t s yz=6 cm. y C 2.4 ft. z v uv=2.4 ft. u SSS Side-side-side: if the two triangles have three congruent sides, then the triangles themselves are congruent. 6 cm. 6 cm. 6 cm. 6 cm. 6 cm. 8 cm. 8 cm. 5 cm. 6 cm. 8 cm. 8 cm. 5 cm. These two triangles are congruent to each other. SAS Side-angle-side: If two sides and the angle in a triangle are congruent to the other two sides and the angle in another triangle, the both triangles are congruent to each other. ASA Angle-side-angle: if the two angles and the side on each triangle are congruent to each other, then the triangles themselves are congruent. AAS Angle-angle-side: If the two angles and the side are congruent, then the triangles themselves are congruent.