SSS Similarity

Q. Two Triangles are similar if corresponding sides are in proportion and corresponding angles are equal. By satisfying one condition is enough to say that triangles are simiar?

Q.

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB.

Q.

If $y=x^2+x^{\log x}$, then $\frac{dy}{dx}=?$

1. $\frac{\left(x^2+\log x{x}^{\log x}\right)}{x}$

2. $2\frac{\left(x^2+\log x{x}^{\log x}\right)}{x}$

3. $\left(x^2+\log x{x}^{\log x}\right)$

4. none of the above

Q.

In $△$ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Find the value of sin P, cos P and tan P.

Q. For two triangles, if sides of one triangle are proportional to the sides of other triangle, then their corresponding angles are equal and hence the two triangles are similar. This is called ___ similarity.

1. $AAA$
2. $SSS$
3. $SAS$
4. none of these

Q.

Prove that the intecept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

Q.

In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form.

(i)

(ii)

(iii)

(iv)

(v)

Q. For two triangles PQR and XYZ, $\frac{PQ}{QR}=\frac{YZ}{ZX}$ and $\frac{QR}{PR}=\frac{ZX}{YX}$ .

1. ∆PQR~ ∆YZX
2. ∆RPQ ~ ∆YZX
3. ∆PQR~∆XYZ

Q. In a triangle ABC, N is a point on AC such that BN ⊥ AC. If BN² = AN . NC, prove that ∠B = 90°.

Q. Question 147
In parallelogram PQRS, O is the mid-point of SQ. Find $\angle S,\angle R$, PQ, QR and diagonal PR.

Q. Question 9
The ratio of the corresponding altitudes of two similar triangles is 3 : 5. Is it correct to say that ratio of their areas is 6 : 5? Why?

Q.

Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding heights.

Q. In an isosceles triangle ABC if AC = BC and AB² = 2AC², then ∠C =

(a) 30°
(b) 45°
(c) 90°
(d) 60°

Q. A point D is on the side BC of an equilateral triangle ABC such that $\mathrm{DC}=\frac{1}{4}\mathrm{BC}$. Prove that AD² = 13 CD².

Q. The given triangles ∆ABC and ∆XYZ are similar, find the length of the side XY.

1. 8 cm
2. 10 cm
3. 12 cm
4. 14 cm

Q. If the corresponding sides of two triangles are proportional, then the two triangles are similar by which test

1. SSS test
2. SAS test
3. AAA test
4. ASA test

Q.

State the SSS-criterion for similarity of triangles.

Q.

In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio 4 : 9, find the ratio of the areas of $△$ABC and $△$PQR.

Q.

If $\Delta MNP\sim \Delta RST$, then the value of x is

1. 24
2. 20
3. 32

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. Question 1 (i)
State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Q.

$\text{Observe the given triangles and find the}\text{value of}\angle P.$

1. ${60}^{\circ }$

2. ${40}^{\circ }$

3. ${50}^{\circ }$

4. ${65}^{\circ }$

Q.

If ∆ABC~∆EDF and ∆ABC is not similar to ∆DEF, then which of the following is not true?

1. BC×DE=AB×FD

2. BC×EF=AC×FD

3. BC×DE=AB×EF

4. AB×EF=AC×DE

Q.

Find the ratio of the areas of two similar triangles ABC and PQR shown in the figure where AM and PN are the medians of the $△$ABC and $△$PQR respectively.

1. AB²/PQ²

2. AM²/PN²

3. Both a and b

4. PQ²/QR²

Q.

$PQ$ and $RS$ bisect each other at $O$ as shown in the figure. Prove that $PR=QS$.

Q.

If $\frac{PQ}{QR}=\frac{YZ}{ZX}$ and $\frac{QR}{PR}=\frac{ZX}{YX}$ , then

1. $△PQR\sim △YZX$

2. $△RPQ\sim △YZX$

3. $△PQR\sim △XYZ$

4. They are not similar

Q. In $△ABC$, AD is the median. Which of these conditions should be satisfied to make $\Delta ADB$ and $\Delta ADC$ similar triangles?

1. $AB=AC$
2. $\angle B=\angle C$
3. $\angle A={90}^{\circ }$
4. (b) or (c) above.

Q. In $\Delta$ ABC, AD is the median and AB = AC. Then by which similarity criterion are $\Delta$ ADB and $\Delta$ ADC similar?

1. SSS
2. AA
3. SAS
4. None of the above

Q.

All ___ triangles are always similar.

1. scalene

2. right angled

3. equilateral

4. isosceles

Q.

If $\Delta ABC\sim \Delta DEF$ such that area of $\Delta ABC$ is $9c{m}^2$ and the area of $\Delta DEF$ is $16c{m}^2$ and BC = 2.1 cm. Find the length of EF. [2 MARKS]