Question

Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

Answer 1

Side ST and side UT are similar by a scale factor of 2.

Angle RTS and angle VTU are similar by verticle angles.

Side RS is similar to side VU by a scale factor of 2.

Answer 2

Find out  statements from the diagram that proves triangles are similar by the SAS similarity theorem

ANSWER

By SAS similarity theorem

If the two right triangles contain corresponding sides through equal ratios, they are said to be similar

take

In the Δ RST and ΔVUT

take

$\frac{UV}{RS} =\frac{6}{12}$

$\frac{UV}{RS} = \frac{1}{2}$

Now take

$\frac{UT}{ST} = \frac{8}{16}$

$\frac{UT}{ST} =\frac{1}{2}$

$\frac{UV}{RS} =\frac{UT}{ST} =\frac{1}{2}$

∠RST = ∠ VUT = 90° ( shown in the diagram )

therefore the triangle shown in diagram i.e Δ RST and ΔVUT are similar   by SAS similarity property.