Question

Please help if you know how to do Similarity in Geometry!!

Answer 1

2. TU, UV and TV are mid-segments

3. Definition of mid-segment

4. Division property of equality

6. SSS similarity theorem

Solution:

Step 1: Given

T is the midpoint of QR.

U is the midpoint of QS.

V is the midpoint of RS.

Step 2: Mid-segments connects midpoints of opposite sides.

TU, UV and TV are mid-segments.

Step 3: By definition of mid-segment

A triangle mid-segment is parallel to the third side of the triangle and is half of the length of the third side.

$T U=\frac{1}{2} R S,$ ${U V}=\frac{1}{2} {Q} R$ and $V T=\frac{1}{2} S Q$

Step 4: By division property of equality

Divide first segment by RS, second segment by QR and third segment by SQ.

$\frac{T U}{R S}=\frac{1}{2}, \ \frac{U V}{Q R}=\frac{1}{2}, \ \frac{V T}{S Q}=\frac{1}{2}$

Step 5: By transitive property

$\frac{T U}{R S}=\frac{U V}{Q R}=\frac{V T}{S Q}$

Step 6: From the above steps, the sides of the triangle are congruent.

By SSS similarity theorem,

$\Delta \text { QRS } \sim \Delta \text { VUT }$

Hence proved.