Question

In the figure above, if 11 perp12 and 13 / 14,. Which of the following statements must be true? I.a+b=90 II. a + c = 90 III. b=dA. I onlyB. II onlyC. I and II onlyD. II and III only

Answer 1

From the given figure

Since l3 // l4, then

a = d ----- corresponding angle

b = c ----- corresponding angles

Since l1 is perpendicular to l2, then

In the small triangle

a + b = 180 - 90

a + b = 90 degrees

In the big triangle

d + c = 180 - 90

d + c = 90 degrees

Let us look at the correct statements

I. a + b = 90 is correct

II. a + c = 90

Since b = c

Then replace b by c in I, then

a + c = 90 is correct

III. b = d is false

Then the correct statements are I and II

The answer is C