Question

the two triangles in the diagram are similar there are two possible values of x. work out each of these values. State both assumptions you make in your working

Answer 1

Answer ⤵️

By changing the order of vertices,

We have four conditions,

When we have or ,

Then by the property of similar angles,

⇒

⇒

⇒

⇒

⇒ x = 2

But, or is given,

Then by the property of similar triangles,

⇒

⇒

⇒

⇒

⇒ x = 17

Note: is reflexive angle in both triangles this is why, in each condition we took A is corresponding to A.

Answer 2

Answer: here it is

Step-by-step explanation:

If abe is similar to acd, sf= 18/15

SF=1.2

AC=1.2 times 10= 12

12-10=2

x=2cm

If abe is similar to adc, sf= 18/10

SF= 1.8

AC= 1.8 times 15= 27

27-10=17

x= 17cm