Math Problem Statement

Construct the triangle ABC such that AB = 7 cm, BC = 5 cm, and ∠ABC = 60°. Then construct the perpendicular bisector of AC, label the intersection point as D where AD = CD = 6.5 cm. Draw a parallel line to AC through D and label the intersection point as E. Prove that triangle BCE is congruent to triangle ABCD.

Solution

The image appears to present a geometric construction problem involving a triangle, quadrilateral, and a series of steps for creating specific constructions. Here's the task breakdown:

  1. Construct the triangle ABC with the given dimensions:

    • AB = 7 cm
    • BC = 5 cm
    • ∠ABC = 60°

  2. Construct the perpendicular bisector of AC, and label the intersection point as D. The length of AD = CD = 6.5 cm.

  3. Draw a parallel line to AC through D, and name the point where the perpendicular bisector intersects this parallel line as E.

  4. Prove that triangle BCE is congruent to triangle ABCD, which is a quadrilateral.

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Math Problem Analysis

Mathematical Concepts

Geometry
Congruence of Triangles
Perpendicular Bisector
Parallel Lines

Formulas

-

Theorems

Congruence of Triangles (SSS, SAS, ASA)
Properties of Perpendicular Bisectors
Parallel Line Postulate

Suitable Grade Level

Grades 9-11

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