Download App

Mid - point Theorem and Intercept Theorem MATHEMATICS - Mid - point Theorem and Intercept Theorem

ICSE - STD 9 - MATHEMATICS (ICSE - English Medium). 66 questions in this chapter.

Question types

Mid - point Theorem and Intercept Theorem question types

66 questions across 5 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.

66
Questions
5
Question groups
5
Question types
Sample Questions

Mid - point Theorem and Intercept Theorem questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1[2 Mark Question Answer]2 Marks
In the adjoining figure, ABCD is a kite in which $AB = AD$ and $CB = CD$. If $E , F , G$ are respectively the mid-points of $AB , AD$ and CD , prove that:
(i) $\angle EFG =90$,
(ii) If $GH \| FE$, then H bisects CB .
Image
View full solution →
Q 2[2 Mark Question Answer]2 Marks
In the adjoining figure, ABCD is a parallelogram in which E is the mid-point of DC and F is a point on AC such that $CF =\frac{1}{4} AC$. If EF is produced to meet BC in G , prove that G is the mid-point of BC .
Image
View full solution →
Q 3[2 Mark Question Answer]2 Marks
In the given figure, LMN is a right triangle in which $\angle M =90$, P and Q are mid-points of LM and LN respectively. If $LM =9 cm, MN =12 cm$ and $LN =15 cm$, find :
(i) the perimeter of trapezium MNQP,
(ii) the area of trapezium MNQP.
Image
View full solution →
Q 4[2 Mark Question Answer]2 Marks
In the given figure $A , B , C$ and D are midpoints of PQ, QR, RS and PS respectively. $E , F , G$ and H are mid-points of $AB , BC$, CD and AD respectively. Which type of quadrilaterals are ABCD and EFGH ?
Image
View full solution →
Q 5[2 Mark Question Answer]2 Marks
In the given figure, $\triangle A B C$ is a scalene triangle in which $\angle B =90 . P$ is the midpoint of $AB , PQ \| BC$ and $QM \perp BC$. Which type of quadrilateral is PQMB ?
Image
View full solution →
Q 6[3 marks sum]3 Marks
In the adjoining figure, ABCD is a parallelogram, E is the mid-point of CD and through D, a line is drawn parallel to EB to meet CB produced at G and intersecting AB at F .
Prove that:
(i) $AD =\frac{1}{2} GC$
(ii) $DG =2 EB$.
Image
View full solution →
Q 7[3 marks sum]3 Marks
If $D , E , F$ are respectively the mid-points of the sides $AB , BC$ and CA of an equilateral triangle ABC , prove that $\triangle DEF$ is also an equilateral triangle.
View full solution →
Q 8[3 marks sum]3 Marks
In the given figure, D, E, F are respectively the midpoints of the sides $AB , BC$ and CA of $\triangle ABC$. Prove that ADEF is a parallelogram.
Image
View full solution →
Q 10[3 marks sum]3 Marks
In the adjoining figure, ABCD is a trapezium in which $AB \| DC$ and E is the mid-point of AD . If $EF \| AB$ meets BC at F , show that F is the mid-point of BC .
Image
View full solution →
Q 11[4 marks sum]4 Marks
In the adjoining figure, in $\triangle ABC , AD$ is the median through A and E is the mid-point of AD . If BE produced meets AC in F , prove that $AF =\frac{1}{3} AC$.
Image
View full solution →
Q 12[4 marks sum]4 Marks
In the adjoining figure, ABCD is a quadrilateral in which $AD = BC$ and $P , Q , R , S$ are the mid-points of $AB , BD , CD$ and $A C$ respectively. Prove that $P Q R S$ is a rhombus.
Image
View full solution →
Q 13[4 marks sum]4 Marks
Two points A and B lie on the same side of a line XY . If $AD \perp XY$ and $BE \perp XY$ meet XY in D and E respectively and $C$ is the mid-point of $A B$, show that $CD = CE$.
Image
View full solution →
Q 14[4 marks sum]4 Marks
Two points $A$ and $B$ lie on the same side of a line $X Y$. If $AD \perp XY$ and $BE \perp XY$ meet XY in D and E respectively and $C$ is the mid-point of $A B$, show that $CD = CE$.
Image
View full solution →
Q 15[4 marks sum]4 Marks
In the adjoining figure, in $\triangle ABC , AD$ is the median through A and E is the mid-point of AD . If BE produced meets AC in F , prove that $AF =\frac{1}{3} AC$.
Image
View full solution →
Q 16[5 marks sum]5 Marks
Ankita took part in a Rangoli Competition. She made a beautiful Rangoli in the shape of a triangle ABC as shown. In the triangle, P, Q and R are mid-points of the sides AB, BC and CA respectively. She decorated it by putting a garland along the sides of Delta*PQR The lengths of the sides of the triangle are AB = 20 cm, BC = 26 cm and AC = 24 cm.
Image
Based on the above information, answer the following questions :
Q.1. The length of AP is :
(a) QB (b) QR (c) AR (d) RP
Q.2. The length of PQ is :
(a) 12 cm (b) 13 cm (c) 10 cm (d) 15 cm
Q.3. The length of the garland is :
(a) 30 cm (b) 32 cm (c) 35 cm (d) 40 cm
Q.4. Area of $\triangle PQR$ is :
(a) area of $\triangle ABC$ (b) $\frac{1}{2}$ area of $\triangle ABC$ (c) $\frac{1}{3}$ area of $\triangle ABC$ (d) $\frac{1}{4}$ area of $\triangle ABC$
Q.5. APQR is a :
(a) rectangle (b) parallelogram (c) square (d) rhombus
View full solution →
Q 17[5 marks sum]5 Marks
Image
Case Study : Ankita took part in a Rangoli Competition. She made a beautiful Rangoli in the shape of a triangle ABC as shown. In the triangle, $P, Q$ and $R$ are mid-points of the sides $A B, B C$ and $C A$ respectively. She decorated it by putting a garland along the sides of $\triangle PQR$. The lengths of the sides of the triangle are $AB =20 cm, BC$ $=26 cm$ and $AC =24 cm$.
Based on the above information, answer the following questions:
Based on the above information, answer the following questions:
1. The length of AP is :
(a) QB
(b) QR
(c) $A R$
(d) RP
2. The length of $P Q$ is :
(a) 12 cm
(b) 13 cm
(c) 10 cm
(d) 15 cm
3. The length of the garland is :
(a) 30 cm
(b) 32 cm
(c) 35 cm
(d) 40 cm
4. Area of $\triangle PQR$ is :
(a) area of $\triangle ABC$
(b) $\frac{1}{2}$ area of $\triangle ABC$
(c) $\frac{1}{3}$ area of $\triangle ABC$
(d) $\frac{1}{4}$ area of $\triangle ABC$
5. APQR is a :
(a) rectangle
(b) parallelogram
(c) square
(d) rhombus
View full solution →
Q 18MCQ1 Mark
In the figure, R is the mid-point of AB, P is the mid-point of AR and L is the mid-point of AP. If RS, PQ and LM are parallel to each other, then the length of BC is:
Image
  • A
    3 LM
  • B
    4 LM
  • C
    6 LM
  • ✓
    8 LM

Answer: D.

View full solution →
Q 19MCQ1 Mark
In which of the following cases you will get $2 XY = QR$ for the given figure?
(i) When $PX = QX$ and $PY = RY$
(ii) When $PX = QX$ and $a+b=180$.
Image
  • A
    Only in case (i)
  • B
    Only in case (ii)
  • ✓
    In both the cases
  • D
    None of these

Answer: C.

View full solution →
Q 20MCQ1 Mark
D and E are the mid-points of the sides AB and AC respectively of ABC. DE is produced to F. To show that CF is equal and parallel to DA, we need an additional information, which is:
  • ✓
    $DE = EF$
  • B
    $AE = EF$
  • C
    $\angle DAE =\angle EFC$
  • D
    $\angle ADE =\angle ECF$

Answer: A.

View full solution →
Q 21MCQ1 Mark
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order is a square only, if:
  • A
    ABCD is a rhombus
  • B
    diagonals of ABCD are equal
  • ✓
    diagonals of ABCD are equal and perpendicular
  • D
    diagonals of ABCD are perpendicular

Answer: C.

View full solution →
Q 22MCQ1 Mark
Assertion (A) : The mid-points of the sides of a quadrilateral ABCD are joined in order to get quadrilateral PQRS. PQRS is a rhombus.
Reason (R) : Adjacent sides of a rhombus are equal and perpendicular to each other.
Image
  • A
    A is true, R is false
  • B
    A is false, R is true
  • C
    Both A and R are true
  • ✓
    Both A and R are false.

Answer: D.

View full solution →
Browse all question groups ↑

Generate a Mid - point Theorem and Intercept Theorem paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App
Generate Paper FreeAll MATHEMATICS chapters