MCQ 11 Mark
Statement-1 (A): $ A B C D$ is a trapezium with $D C \| A B, E$ and $F$ are points on $A D$ and $B C$ respectively, such that $E F \| A B$. Then, $\frac{A E}{E D}=\frac{B F}{F C}$.
Statement-2 (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
View full question & answer→MCQ 21 Mark
Statement-1 (A) : If in $\triangle A B C, D$ and $E$ are points on sides $A B$ and $A C$ respectively such that $D E \| B C$, then $\frac{A D}{A B}=\frac{A E}{A C}$.
Statement-2 (R): If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
AnswerCorrect option: A. Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
We find that statement-2, being well known BP T, is true. Using statement- 2 , we obtain
$
\begin{array}{ll}
& \frac{A D}{D B}=\frac{A E}{E C} \\
\Rightarrow & \frac{D B}{A D}=\frac{E C}{A E} \\
\Rightarrow & \frac{D B}{A D}+1=\frac{E C}{A E}+1 \\
\Rightarrow & \frac{D B+A D}{A D}=\frac{E C+A E}{A E} \Rightarrow \frac{A B}{A D}=\frac{A C}{A E} \Rightarrow \frac{A D}{A B}=\frac{A E}{A C}
\end{array}
$
So, statement-1 is true. Also, statement-2 is a correct explanation for statement-1.
Hence, option (a) is correct. View full question & answer→MCQ 31 Mark
Slatement-1 (A): Let $\triangle A B C$ and $\triangle D E F$ be right triangles right angled at $B$ and $E$ respectively. If $A C=5 cm, B C=4 cm, D F=15 cm$ and $E F=12 cm$, then $\angle A=\angle D$ and $\angle C=\angle F$.
Statement-2 (R): If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the triangles are similar.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
AnswerCorrect option: A. Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
Statement-2 is the RHS-similarity criterion, so it is true.
In right triangles $A B C$ and $D E F$, we find that $A C$ and $D F$ are hypotenuse such that $\frac{A C}{D F}=\frac{B C}{E F}=\frac{1}{3}$. Therefore, by using statement-2, we obtain
$
\triangle A B C \sim \triangle D E F \Rightarrow \angle A=\angle D \text { and } \angle C=\angle F
$
So, statement- 1 is also true and statement- 2 is a correct explanation for statement- 1 .
Hence, option (a) is correct.
View full question & answer→MCQ 41 Mark
Statement-1 (A): In $\triangle A B C$, if $A B=24 cm, B C=10 cm$ and $A C=26 cm$, then $\triangle A B C$ is a right angled triangle.
Statement-2 (R): If corresponding sides of two triangles are equal, then the triangles are similar.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
AnswerCorrect option: B. Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
(B)Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
We find that in $\triangle A B C, A C^2=A B^2+B C^2$ holds good.
Thus, by using the converse of Pythagoras theorem, $\triangle A B C$ is a right angled triangle. So, statement-1 is true.
Let $A B C$ and $P Q R$ be two triangles such that their corresponding sides are equal i.e. $A B=P Q$, $B C=Q R$ and $A C=P R$. Then,
$
\frac{A B}{P Q}=\frac{B C}{Q R}=\frac{A C}{P R} \Rightarrow \triangle A B C \sim \triangle P Q R
$
So, statement-2 is true. But, it is not a correct explanation for statement-1.
Hence, option (b) is correct.
View full question & answer→MCQ 51 Mark
Statement-1 (A): Let $\triangle P Q R$ be a right triangle right angled at $Q$ such that the perpendicular drawn from $Q$ on hypotenuse $P R$ meets $P R$ at $S$. If $P S=4$ cm and $R S=9 cm$, then $Q S=6 cm$.
Statement-2 (R): In a right triangle, the square of the perpendicular drawn from the vertex forming right angle to the hypotenuse is equal to the product of projections of two sides on the hypotenuse.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
AnswerCorrect option: A. Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
Let $A B C$ be a right triangle right angled at $A$ and $A D$ be perpendicular drawn from $A$ on hypotenuse $B C$.
In $\triangle$ 's $A D B$ and $C D A$, we have
$\angle A D B=\angle C D A$ $\qquad$ [Each equal to $90^{\circ}$ ]
and, $\quad \angle D A B=\angle D C A$
So, by using $A A$-criterion of similarity, we obtain
$
\triangle A D B \sim \triangle C D A \Rightarrow \frac{A D}{C D}=\frac{D B}{D A} \Rightarrow A D^2=B C \times C D
$
Thus, statement-2 is true. Using statement-2, we find that in $\triangle P Q R$.
$
Q S^2=P S \times R S \Rightarrow Q S^2=4 \times 9=36 \Rightarrow Q S=6 cm
$
So, statement- 1 is also true and statement- 2 is a correct explanation for statement- 1 .
Hence, option (a) is correct. View full question & answer→MCQ 61 Mark
Statement-1 (A): In Fig. if $A B \| C D$, then $x=3$.
Statement-2 (R): Diagonals of a trapezium divide each other proportionally.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
View full question & answer→MCQ 71 Mark
Statement-1 (A): $D$ and $E$ are points on sides $A B$ and $A C$ of $\triangle A B C$ such that $A D=(7 x-4) cm$, $A E=(5 x-2) cm , D B=(3 x+4) cm$ and $E C=3 x cm$. If $D E \| B C$, then $x=5$.
Statement-2 (R): If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: D. Statement-1 is false, Statement-2 is true.
View full question & answer→MCQ 81 Mark
Statement-1 (A): In two triangles, if corresponding angles are equal then the triangles are similar.
Statement-2 (R): If the areas of two similar triangles are equal, then the triangles are congruent.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: B. Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
View full question & answer→MCQ 91 Mark
Statement-1 (A): In $\triangle P Q R$, if $P Q=12 cm, Q R=9 cm$ and $P R=15 cm$, then $\triangle P Q R$ is a right triangle right angled at $Q$.
Statement-2 (R): If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
View full question & answer→MCQ 101 Mark
Statement-1 (A): If $\triangle A B C$ and $\triangle P Q R$ are right triangles right angled at $C$ and $R$ respectively such that $\frac{A B}{P Q}=\frac{A C}{P R}$, then $\angle B=\angle Q$.
Statement-2 (R): If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the two triangles are similar.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- D
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
View full question & answer→MCQ 111 Mark
Statement-1 (A): Two similar triangles are always congruent.
Statement-2 (R): Two congruent triangles are always similar.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
AnswerCorrect option: D. Statement-1 is false, Statement-2 is true.
View full question & answer→