Mathematics

Mathematics

Problem

In

\triangle ABC

,

\angle C = 90^{\circ}

and the two legs are equal,

AC = BC = 10\,\text{cm}

. The perpendicular from

C

meets

AB

at

D

. a. (a) Prove that

\triangle ACD \cong \triangle BCD

. b. (b) Find the length of

CD

. c. (c) Determine the lengths of

AD

and

BD

. d. (d) Calculate the area of

\triangle ABC

. (Leave

\sqrt{}

terms if necessary.)

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