Two triangles ABC and PQR are such that AB - 3 cm- AC - 6 cm- - A - 70o-PR - 9 cm- P - 70o-and -PQ - 4-5 cm- Show that - ABC - PQR and state the similarity criterion-

AB/PQ=3/4.5=2/3 AC/PR=6/9=2/3 AB/PQ=AC/PR=2/3 ∠ A=∠ P=70 Thus triangle ABC and PQR are similar ...

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Mathematics

Criteria for Similarity of Triangles

Two triangles...

Question

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.

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Solution

$\frac{A B}{P Q}$ = $\frac{3}{4.5}$ = $\frac{2}{3}$

$\frac{A C}{P R}$ = $\frac{6}{9}$ = $\frac{2}{3}$

$\frac{A B}{P Q}$ = $\frac{A C}{P R}$ = $\frac{2}{3}$
$∠ A = ∠ P = 70$
Thus triangle ABC and PQR are similar

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Similar questions

Q. Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A = 70⁰ PR = 9 cm, ∠P = 70⁰ and PQ = 4.5 cm. Show that
△ABC ∼ △PQR and state similarity theorem.

Q. Match the column.

1. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R}, ∠ A = ∠ P$	(a) AA similarity criterion
2. In $Δ A B C$ and $Δ P Q R$ , $∠ A = ∠ P, ∠ B = ∠ Q$	(b) SAS similarity criterion
3. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R} = \frac{B C}{Q R}$ $∠ A = ∠ P$	(c) SSS similarity criterion
4. In $Δ A C B, D E \| \| B C$ $\Rightarrow \frac{A D}{B D} = \frac{A E}{C E}$	(d) BPT

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

Δ A B C \sim Δ P Q R

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. Question 14
Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that

Δ A B C \sim Δ P Q R

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Two triangles ABC and PQR are such that AB = 3 cm, AC = 6 cm, ∠A=70o, PR=9cm, ∠P=70o and PQ=4.5cm. Show that ΔABC∼ΔPQR and state the similarity criterion.

ABPQ=34.5=23 ACPR=69=23 ABPQ=ACPR=23 ∠A=∠P=70 Thus triangle ABC and PQR are similar

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.

$\frac{A B}{P Q}$ = $\frac{3}{4.5}$ = $\frac{2}{3}$

$\frac{A C}{P R}$ = $\frac{6}{9}$ = $\frac{2}{3}$

$\frac{A B}{P Q}$ = $\frac{A C}{P R}$ = $\frac{2}{3}$
$∠ A = ∠ P = 70$
Thus triangle ABC and PQR are similar