# SAS Similarity

## Trending Questions

**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 ΔABC∼ΔPQR.

**Q.**Question 1

If two lines intersect, prove that the vertically opposite angles are equal.

**Q.**In the given figure ABC is a right-angled triangle with ∠BAC=90∘ [4 MARKS]

i) Prove that ΔADB∼ΔCDA

ii) IF BD = 18 cm, CD = 8 cm, find AD

iii) Find the ratio of the area of ΔADB is to area of ΔCDA

**Q.**

**Question 13**

If an isosceles Δ ABC in which AB = AC = 6cm, is inscribed in a circle of radius 9 cm, find the area of the triangle.

**Q.**

The angle between the two lines $y-2x=9\text{and}x+2y=7,$ is

$60\xc2\xb0$

$30\xc2\xb0$

$90\xc2\xb0$

$45\xc2\xb0$

**Q.**Question 12

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that ΔABC∼ΔPQR.

**Q.**

$D$ is a point on the side $BC$of a triangle$ABC$ such that $\xe2\u02c6ADC=\xe2\u02c6BAC.$ Show that $C{A}^{2}=CB.CD$

**Q.**

CM and RN are respectively the medians of ΔABC and ΔPQR. If ΔABC∼ΔPQR, prove that:

(i) ΔAMC∼ΔPNR

(ii) CMRN=ABPQ

(iii) ΔCMB∼ΔRNQ

[3 MARKS]

**Q.**

If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR$, respectively where $\mathrm{\xce\u201d}ABC~\mathrm{\xce\u201d}PQR$ prove that $\frac{AB}{PQ}=\frac{AD}{PM}$.

**Q.**

In a triangle, the lengths of two larger sides are $10cm$and $9cm$. If the angles of the triangle are in AP, then the length of the third side is:

$\sqrt{5}-\sqrt{6}$

$\sqrt{5}+\sqrt{6}$

$\sqrt{5}\xc2\pm \sqrt{6}$

$5\xc2\pm \sqrt{6}$

**Q.**

It is given that $\mathrm{\xce\u201d}DEF~\mathrm{\xce\u201d}RPQ$. Is it true to say that $\xe2\u02c6D=\xe2\u02c6R$ and $\xe2\u02c6F=\xe2\u02c6P$? Why?

- True
- False

**Q.**Question 5

In figure, two line segments AC and BD intersect each other at the point P such that PA=6cm, PB=6cm, PC=3cm, PC=2.5cm, PD=5cm, ∠APB=50∘ and ∠CDP=30∘ .Then ∠PBA is equal to

(A) 50∘

(B) 30∘

(C) 60∘

(D) 100∘

**Q.**

In an isosceles ΔABC, the base AB has produced both ways in P and Q such that AP×BQ=AC2.

Prove that ΔACP∼ΔBCQ.

**Q.**

Calculate the percentage of p-character in the orbital occupied by the lone pairs in water molecules : [Given:âˆ HOH is 104.5âˆ˜ and cos (104.5)= âˆ’ 0.25]

**Q.**Question 4

In the figure,

QRQS=QTPR and

∠1=∠2.

Show that ΔPQS∼ΔTQR.

**Q.**Question 12

Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.

**Q.**ABC is a right-angled triangle with ∠ABC=90∘. D is any point on AB and DE is perpendicular to AC. Prove that: [4 MARKS]

i) ΔADE∼ΔACB

ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm, find DE and AD.

iii) Find, area of ΔADE : area of quadrilateral BCED

**Q.**Question 16

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC∼ΔPQR. Prove that ABPQ=ADPM.

**Q.**Question 5

To construct a triangle similar to a given ΔABC with its sides 85 of the corresponding sides of ΔABC draw a ray BX such that ∠ CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is

(A) 5

(B) 8

(C) 13

(D) 3

**Q.**

In the given figure, ∠1=∠2 and ACBD=CBCE.

Prove that ΔACB∼ΔDCE.

**Q.**

**Question 4**

In the following figure, DE||AC and DF||AE. Prove that BFFE=BEEC .

**Q.**

State the SAS-similarity criterion.

**Q.**

In triangle ABC, points D and E lie on sides AB and AC respectively such that DE is parallel to BC.

If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE is equal to ____.

1.4 cm

1.05 cm

1.8 cm

1.2 cm

**Q.**In the given figure, ∠QPS=∠RPTand∠PRQ=∠PTS. [4 MARKS]

(i) Prove that ΔPQR∼ΔPST

(ii) If PT:ST=3:4, find QR : PR.

**Q.**A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight and describes 88 metres when it has traced out 72o at the center, find the length of the rope.

**Q.**The two triangles are congruent by _________ congruency rule.

- SSS
- SAS
- RHS
- ASA

**Q.**

Triangle ABC is similar to triangle PQR. If AD and PM are corresponding medians of the two triangles, prove that : ABPQ=ADPM.

**Q.**In the given figure, ∠GHE=∠DFE=90∘, DH=8 cm, DF=12 cm, DG=(3x−1) cm and DE=(4x+2)cm. find the length of segments DG and DE.

[4 MARKS]

**Q.**

**Question 3**

In the following figure, if LM || CB and LN || CD, prove that AMAB=ANAD.

**Q.**

**Question 15**

O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with ABIIDC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that PO = QO.