Geometry Problem: Prove Triangle is Isosceles and Angle Relationships

Math Problem Statement

solve

In the diagram, PQT is a straight line and SQ // RT. (a) Join QR and show that: (i) ∠RPS = ∠QRT; (ii) ∠PRS = ∠QTR. (b) ABC is a triangle. The sides AB and AC are produced to D and E respectively such that ∠DBC = 132° and ∠ECD = 96°. Show that ΔABC is isosceles.

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines and Transversals
Triangle Properties
Isosceles Triangle Theorem

Formulas

Sum of angles in a triangle = 180°
Exterior angle of a triangle = sum of two opposite interior angles

Theorems

Alternate Angles Theorem
Base Angles Theorem (for Isosceles Triangles)

Suitable Grade Level

Grades 9-10

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