Question

Number 3 “determine whether the triangles are similar if they are write a similarity statement if not explain what would be sufficient to prove the triangles similar”

Answer 1

By 'AAA Similarity Postulate', ΔSTR ≅ ΔSWX.

Explanation:

We are given isosceles triangles ΔSTR and ΔSWX with ∠TSR=∠WSX.

Since, sides ST=SR and SW=SX, then their opposite angles will be equal.

So, we get,

∠STR=∠SRT and ∠SWX=∠SXW.

Now, as 'the sum of angles in a triangle is 180°'.

So, we get,

∠TSR + 2∠STR = 180°

2∠SWX + ∠WSX = 180°

As, ∠TSR=∠WSX, this gives, ∠STR = ∠SRT = ∠SWX = ∠SXW.

So, using 'AAA Similarity Postulate', we get that, ΔSTR ≅ ΔSWX.

Answer 2

Explanation:

Given are triangles WSX and TRS

The two lines namely RW and TX intersect at point S thus making two triangles

From the given information we find that

angle TSR = angleWSX(vertically opposite angles)

But this is not sufficient to prove that two triangles are similarl. Atleast two angles must be congruent

Hence we must have information as angle RST = angle SWX or angle TRS=angleWXS to prove these are similar

Or angle RST =angle SXW or two lines TR||WX to complete the proof