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Find BC and AC.įigure 3 An equiangular triangle with a specified side.īecause the triangle is equiangular, it is also equilateral.

If m ∠ Q = 50°, find m ∠ R and m ∠ S.įigure 2 An isosceles triangle with a specified vertex angle.īecause m ∠ Q + m ∠ R + m ∠ S = 180°, and because QR = QS implies that m ∠ R = m ∠ S,Įxample 2: Figure 3 has Δ ABC with m ∠ A = m ∠ B = m ∠ C, and AB = 6. Theorem 35: If a triangle is equiangular, then it is also equilateral.Įxample 1: Figure has Δ QRS with QR = QS. Theorem 34: If two angles of a triangle are equal, then the sides opposite these angles are also equal. Theorem 33: If a triangle is equilateral, then it is also equiangular. Theorem 32: If two sides of a triangle are equal, then the angles opposite those sides are also equal. With a median drawn from the vertex to the base, BC, it can be proven that Δ BAX ≅ Δ CAX, which leads to several important theorems. Consider isosceles triangle ABC in Figure 1.įigure 1 An isosceles triangle with a median. In the above figure, triangle ADB and triangle ADC are. Isosceles triangles are special and because of that there are unique relationships that involve their internal line segments. The altitude from the vertex divides an isosceles triangle into two congruent right-angled triangles. Summary of Coordinate Geometry Formulas.You may need to tinker with it to ensure it makes sense. The converse of a conditional statement is made by swapping the hypothesis (if ) with the conclusion (then ). Slopes: Parallel and Perpendicular Lines Converse of the Isosceles Triangle Theorem.It is not a problem to calculate an isosceles triangle, for example, from its area and perimeter ( T12 p16 ). Our calculator provides the calculation of all parameters of the isosceles triangle if you enter two of its parameters, e.g. Similar Triangles: Perimeters and Areas An isosceles triangle is a triangle that has two sides of equal length.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.

Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.