Isosceles right triangle with an angle bisector

Isosceles right triangle with an angle bisector

Secondary 2
TGM Original Questions

Triangle \(ABC\) is right-angled isosceles at \(C\), with \(AC=BC\). Point \(D\) lies on \(CB\), \(DE\perp AB\), and \(AD\) bisects \(\angle CAB\).

  1. Name a pair of congruent triangles.
  2. Name a triangle similar to \(BED\).
  3. Show that \(BED\) is isosceles.
  4. If \(AB=24\) cm, find the perimeter of \(BED\).

Solution:

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Answer:(a) \(\triangle ACD\cong\triangle AED\); (b) \(\triangle BCA\); (c) \(BE=DE\); (d) \(24\) cm.

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