In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find: a Find CD, if BC = 3 in

Mathematics

1 answer:

Elodia [21]2 years ago

6 0

Answer:

CD = (3/2)√2

Step-by-step explanation:

All the triangles are similar isosceles right triangles, so the hypotenuse in each case is √(1²+1²) = √2 times the length of the corresponding legs. BC is the hypotenuse of ΔBCD, so leg CD is that length divided by √2.

CD = BC/√2 = 3/√2

CD = (3/2)√2

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i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money

valkas [14]

Answer:

Step-by-step explanation:

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7 0

2 years ago

I really am confused on how to write a proof.

kvasek [131]

Since ABCD is a parallelogram, the opposite sides will be parallel and equal,

$\begin{gathered} AB=CD \\ BC=AD \end{gathered}$

Consider that AC acts as a transversal to the parallel lines AB and CD, so we can write,

$\begin{gathered} \angle CAD=\angle ACB\text{ (Alternate Interior Angles)} \\ BC=AD\text{ (Opposite sides of parallelogram)} \\ \angle ADB=\angle CBD\text{ (Alternate Interior Angles)} \end{gathered}$

So by the ASA criteria, the triangle AED is congruent to the triangle CEB,

Then the corresponding parts of the triangles will be equal,