Show that the two triangles given beside are similar and calculate the lengths of sides PQ and PR.

Open in App

Solution

$∠ A = ∠ P$ and $∠ B = ∠ Q$ ,
$∠ C = ∠ R$ ........(because $∠ C = 180 - ∠ A - ∠ B$ and $∠ R = 180 - ∠ P - ∠ Q$ )

Therefore, the two triangles $Δ A B C$ and $Δ P Q R$ are similar by $A A A$ condition.

So, in similar triangles:

$\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{A C}{P R}$

Hence,
$\frac{6}{12} = \frac{7}{P R} ⟹ P R = \frac{7 \times 12}{6} = 14$

And,
$\frac{6}{12} = \frac{4}{P Q} ⟹ P Q = \frac{4 \times 12}{6} = 8$

Suggest Corrections

Similar questions

Q. In the figure given below,

∠ P Q R = ∠ P R S

. Prove that triangles

P Q R

and

P R S

are similar. If

P R = 8 c m, P S = 4 c m

, calculate

P Q

Sides AB and AC and median AD of triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR . Show that triangle ABC is similar to triangle PQR.

Q. Find the length of the side

P R

and

Q R

if the

△ A B C

is similar to

△ P Q R

and

\frac{A B}{P Q} = \frac{A C}{P R}

Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, $∠ A = 70^{o}, P R = 9 c m, ∠ P = 70^{o} a n d P Q = 4.5 c m$ . Show that $Δ A B C \sim Δ P Q R$ and state the similarity criterion.

S

and

T

are respectively the mid points of equal sides

P Q

and

P R

△ P Q R

. Show that

Q t = R S

Join BYJU'S Learning Program

Show that the two triangles given beside are similar and calculate the lengths of sides PQ and PR.

∠A=∠P and ∠B=∠Q, ∠C=∠R........(because ∠C=180−∠A−∠B and ∠R=180−∠P−∠Q)Therefore, the two triangles ΔABC and ΔPQR are similar by AAA condition.So, in similar triangles:ABPQ=BCQR=ACPRHence,612=7PR⟹PR=7×126=14And,612=4PQ⟹PQ=4×126=8