can you help me with ths maths proof's?

Question

abc is an isoceles triangle with |ab|=|ac|.
[ba] is produced to d, so that |ad|=|ab|.
By joining d to c, prove that |angle bcd|=90 degree's.
can you plz try to explain it in points how to prove this.
Txs

Answer 1

The triangle acd is also an isoceles triangle. Therefore, angles acd and adc are equal.

You also have angle abc=angle acb. Because bac=180-2*abc, you have dac=2*acb.

Since dac+acd+adc=180, and acd=adc, you have 2*acb+2*acd=180. Therefore, acb+acd=90. But this is the angle bcd you're looking for.

Answer 2

Let the angle BAC = x

The angles ABC and BCA have to be equal because it's an isosceles triangle. Therefore:

ABC = BCA = (180-x)/2 = 90-x/2

When you draw line AD, you create another isosceles triangle with AC = AD. The angle DAC must equal 180-x because DAC + BAC must equal 180. Once again because the new triangle is an isosceles triangle:

ACD = ADC = (180 - DAC)/2
ACD = ADC = (180 - (180-x))/2
ACD = ADC = (180 - 180 + x)/2
ACD = ADC = x/2

Angle BCD = BCA + ACD
BCD = 90-x/2 + x/2

BCD = 90

Answer 3

I can try-
Draw the figure. You will see that angle bcd is comprised of angle bca and angle acd. You will also see that the other two angles in the big triangle bcd are congruent respectively to angle bca and angle acd.

The measures of angles dbc, bcd and cdb add up to 180

which means that since angle bcd is the sum of the other two, this sum must be 90.

Answer 4

In an isosceles triangle at least two sides are of equal length. An isosceles triangle also has two equal internal angles.
a+b+c=180

Answer 5

Start your thinking here:
http://www.math.okstate.edu/~geoset/Projects/Construction/Angela.htm
Then look here:
http://www.math.okstate.edu/~geoset/Projects/Construction/Misti.htm
And you should understand the proof here, in the thumbnails.
http://whyslopes.com/Euclidean-Geometry-Introduction/geom06_Isoceles.html
Good Luck!
I hope this helps