Relation between Sides of Triangle

Q.

In a right angled triangle ABC in which ∠A = ${90}^{\circ }$, If AD $\perp$ BC.

1. ${AB}^2$ = BD × AD.

2. ${AB}^2$ = BC × DC.

3. ${AB}^2$ = BC × BD.

4. ${AB}^2$ = BD × DC.

Q.

Given $△$ DEF $\sim$ $△$ABC. If AB = 4 cm, BC = 2 cm, CA = 3 cm and EF = 4 cm, then the perimeter of $△$DEF is ____ cm.

1. 18

2. 15

3. 16

4. 14

Q. If $\Delta ABC\sim \Delta TUS$, match value of $\frac{AB}{TU}=\frac{AC}{TS}=\frac{BC}{US}$ in each case.

1. 2.5
2. 0.67
3. 0.5

Q.

$\Delta ABC\sim \Delta PQR$

Find the values of y and z.

1. $y=3\sqrt{3}$
2. $y=4\sqrt{3}$
3. $z=6$
4. $z=4$

Q.

$△$ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. What is $AC\times DC$?

1. BC.AB

2. ${BC}^2$

3. ${BD}^2$

4. AB.AC

Q.

In the figure, ABCD is a trapezium in which, AB || DC and $\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}andAB=5cm$. Find the value of CD .

1. 10 cm

2. 15 cm

3. 18 cm

4. 20 cm

Q.

In the figure, $\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}andAB=5cm$. Find the value of CD .

Figure 2.

1. 18 cm

2. 20 cm

3. 10 cm

4. 15 cm

Q. In the figure, ABCD is a trapezium in which, AB || DC and $\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}andAB=5cm$. Find the value of CD .

(2 Marks)

Q.

A man of height y is standing between two buildings with heights x and z respectively as shown in the figure. Then, which of the following statements is true about the relation of the heights?

1. $\frac{1}{x}=\frac{1}{y}+\frac{1}{z}$

2. $x=y=z$

3. $\frac{1}{x}=\frac{1}{y}=\frac{1}{z}$

4. $\frac{1}{x}+\frac{1}{z}=\frac{1}{y}$

Q. The sides of $\Delta \text{ABC}$ have sides AB, BC, AC as $2cm,4cm,\text{and}6cm$ respectively. Find the sides of the larger triangle which is similar to $\Delta \text{ABC}$, if the ratio of corresponding sides is $3$.

1. $6cm,12cm,18cm$
2. $5cm,7cm,9cm$
3. $4cm,6cm,12cm$
4. $8cm,12cm,18cm$

Q. $△ABC$ and $△DEF$ are similar such that $2AB=DE$ and $BC=8cm$. Find $EF$.

1. $16cm$
2. $12cm$
3. $8cm$
4. $4cm$

Q.

Statement 1: In two triangles, if two corresponding angles are equal, it’s not required to check whether the ratio of their corresponding sides is equal or not to state that they are similar.
Statement 2: When two triangles are similar, the ratio of their corresponding sides is equal.

1. Statement 1 is true, statement 2 is true and statement 2 is not the correct explanation for statement 1.

2. Statement 1 and Statement 2 are false.

3. Statement 2 is true and Statement 1 is false.

4. Statement 1 is true, statement 2 is true and statement 2 is the correct explanation for statement 1.

Q. The given two triangles are .

1. congruent
2. similar
3. not similar

Q.

$△$ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. Then find the value of $AC\times DC$.

Q.

ABC and DEF are similar triangles, identify the corresponding sides.

1. BC and DE

2. CA and ED

3. AB and DF

4. AC and DF

Q.

In the given figure, AD divides $\angle BAC$ in the ratio 1:3. Find the value of X and $\angle ADC$ (in degrees).

1. 20${}^{\circ }$, 115${}^{\circ }$

2. 115${}^{\circ }$, 20${}^{\circ }$

3. 30${}^{\circ }$, 125${}^{\circ }$

4. 20${}^{\circ }$, 125${}^{\circ }$