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Problem 121

Given: $\underline{C A} \cong \underline{D B} \cdot \underline{C B} \cong \underline{D A} .\( Prove \)\triangle A B C \cong \triangle B A D$.

Expert verified

In the given problem, we have \(CA \cong DB\) and \(CB \cong DA\). Since AB is a common side of both triangles, we have \(AB \cong AB\). By the Side-Side-Side (SSS) congruence theorem, we can conclude that \(\triangle ABC \cong \triangle BAD\).

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Chapter 8

$\underline{\mathrm{DB}} \cong \underline{\mathrm{EA}}, \underline{\mathrm{AD}} \cong \underline{\mathrm{BE}} .\( Prove: \)\angle \mathrm{DAB} \cong \angle \mathrm{EBA}$

Chapter 8

Prove the median of the base of an isosceles triangle is perpendicular to the base.(In the figure, \(\Delta \mathrm{ABC}\) is isosceles, such that \(\underline{\mathrm{CA}} \cong \underline{\mathrm{CB}}\), and \(\underline{\mathrm{CM}}\) is the median to base \(\underline{\mathrm{AB}}\). Prove \(\underline{C M} \perp \underline{A B}\).)

Chapter 8

Let \(\mathrm{ABC}\) be an equilateral triangle. Let \(\mathrm{D}\) be the midpoint of \(\underline{A B}\). Prove that $\triangle D C B \cong \triangle D C A\(. What kind of triangle is \)\triangle \mathrm{DCB}$ ? What can be said about \(\angle \mathrm{ACD}\) and \(\angle \mathrm{BCD} ?\) (See Figure.)

Chapter 8

Given: \(\mathrm{DC} \cong \mathrm{BA}, \mathrm{AD} \cong \mathrm{CB}\). Prove: \(\triangle \mathrm{ABD} \cong \Delta \mathrm{CDB}\)

Chapter 8

Prove: the median drawn to the base of an isosceles triangle bisects the vertex angle.

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