Sides AB and BC and median AD of atriangle ABC are respectively proportionalto sides PQ and QR and medianPM of
Δ PQR (see Fig. 6.41). Show that
Δ ABC ~ Δ PQR.

Question

Sides AB and BC and median AD of atriangle ABC are respectively proportionalto sides PQ and QR and medianPM of &#x394; PQR (see Fig. 6.41). Show that &#x394; ABC ~ &#x394; PQR.

Philoid · Accepted Answer

Median divides the opposite side

BD = and,

QM =

Given:

=

In ΔABD and ΔPQM,

ΔABD ΔPQM (By SSS similarity)

∠ABD = ∠PQM (Corresponding angles of similar triangles)

In ΔABC and ΔPQR,

∠ABD = ∠PQM (Proved above)

ΔABC ΔPQR (By SAS similarity)

Sides AB and BC and median AD of atriangle ABC are respectively proportionalto sides PQ and QR and medianPM ofΔ PQR (see Fig. 6.41). Show thatΔ ABC ~ Δ PQR.

Sides AB and BC and median AD of atriangle ABC are respectively proportionalto sides PQ and QR and medianPM of
Δ PQR (see Fig. 6.41). Show that
Δ ABC ~ Δ PQR.