![]() ![]() Parallel, Perpendicular and Intersecting Lines.2t = 9 Subtract 4y and add 6 to both sides. ∆JKL is equiangular.Įquiangular ∆ equilateral ∆ 4t – 8 = 2t + 1 Definition of equilateral ∆. y = 18 Subtract 4y and add 6 to both sides.ġ7 Example: 11 Find the value of JL. ∆NPO is equiangular.Įquiangular ∆ equilateral ∆ 5y – 6 = 4y + 12 Definition of equilateral ∆. x = 14 Divide both sides by 2.ġ6 Example: 10 Find the value of y. ∆LKM is equilateral.Įquilateral ∆ equiangular ∆ The measure of each of an equiangular ∆ is 60°. mM = 84°ġ4 The following corollary and its converse show the connection between equilateral triangles and equiangular triangles.ġ5 Example: 9 Find the value of x. (8y – 16) = 6y Subtract 6y and add 16 to both sides. x = 66 Thus mH = 66°ġ3 Example: 8 Find mN and mM. x + x + 48 = 180 Simplify and subtract 48 from both sides. (x + 44) = 3x Simplify x from both sides. ![]() x + x + 22 = 180 Simplify and subtract 22 from both sides. Thus YZ = YX = 20 ft.ġ0 Example: 5 Find mF. Since YZX X, ∆XYZ is isosceles by the Converse of the Isosceles Triangle Theorem. Explain why the length of YZ is the same. If two base angles are congruent, then the triangle is isosceles.Ĩ Example 3: x = 90 – 27 x = 63 Given this right angle. ![]() UVR is congruent to R by the Transitive Property of Congruence. Therefore UV is another transversal proving UVR is congruent to S. ? Yes because corresponding angles R and WVS are congruent proving RT || WV with transversal RS. C Bĥ The Isosceles Triangle Theorem is sometimes stated as “Base angles of an isosceles triangle are congruent.” Reading MathĦ Example 1: Proving Isosceles Triangle Theoremħ Example 2: Yes because base angles are congruent The side opposite the vertex angle is called the base, and the base angles are the two angles that have the base as a side. The vertex angle is the angle formed by the legs. Recall that an isosceles triangle has at least two congruent sides. (6)(D) Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems.ģ Vocabulary: Corollary-a theorem that can be proved easily using another theorem. (6)(B) Prove two triangles are congruent by applying the Side- Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle- Side, and Hypotenuse-Leg congruence conditions. (5)(A) Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools. (1)(C) Select tools, including real objects, manipulatives paper and pencil, and technology as appropriate, and techniques, including mental math, estimations, and number sense as appropriate, to solve problems. Presentation on theme: "Pearson Unit 1 Topic 4: Congruent Triangles 4-5: Isosceles and Equilateral Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007."- Presentation transcript:ġ Pearson Unit 1 Topic 4: Congruent Triangles 4-5: Isosceles and Equilateral Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007Ģ TEKS Focus: (5)(C) Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships. ![]()
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