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=(1)/(2) R S,`
`{U V}=(1)/(2) {Q} R` and
`V T=(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.

`$(T U)/(R S)=(1)/(2), \ (U V)/(Q R)=(1)/(2), \ (V T)/(S Q)=(1)/(2)`

Step 5: By transitive property

`$(T U)/(R S)=(U V)/(Q R)=(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.