Given: AB=AC m∠1=m∠2 AC=15, DC=5 Find: BD, AB

BD= m<1=m<½

AB=m<1=m<1

Step-by-step explanation:

Hope it help

AB = 15

BD = 5

Step-by-step explanation:

Statement|          Reason

1) m<1 = m<2, AB = AC                    |   Given

2) AD = AD                                      | Reflexive property

3) ΔABD = ΔADC                           | Side - angle - side

4) AB = AC =  15                               | Corresponding part of congruent triangles     .                                                     |  are congruent

5) BD = DC = 5                              | Corresponding parts of congruent triangles   .                                                    |    are congruent

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240