In $\triangle ABC, D, E, F$ are the midpoints of $\text{BC}, \text{CA}$ and $\text{AB}$ respectively. Find $\angle FDB$ if $\angle ACB = 115^\circ .$
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Mid-point and Intercept Theorems question types
47 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
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Sample Questions
Mid-point and Intercept Theorems questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the given figure, $PS = 3RS. M$ is the midpoint of $QR.$ If $TR \| MN \| QP,$ then prove that:
$RT =\frac{1}{3} PQ$
View full solution →$RT =\frac{1}{3} PQ$
In $\triangle ABC, D$ and $E$ are the midpoints of the sides $AB$ and $BC$ respectively. $F$ is any point on the side $AC.$ Also, $EF$ is parallel to $AB.$ Prove that $\text{BFED}$ is a parallelogram.
Remark: Figure is incorrect in Question
View full solution →Remark: Figure is incorrect in Question
In a parallelogram $\text{ABCD}, E$ and $F$ are the midpoints of the sides $AB$ and $CD$ respectively. The line segments $AF$ and $BF$ meet the line segments $DE$ and $CE$ at points $G$ and $H$ respectively Prove that$: \triangle GEA \cong \triangle GFD$
View full solution →In parallelogram $\text{PQRS, L}$ is mid$-$point of side $SR$ and $SN$ is drawn parallel to $LQ$ which meets $RQ$ produced at $N$ and cuts side $PQ$ at $M.$ Prove that $M$ is the mid$-$point of $PQ.$
View full solution →In $\triangle ABC, D, E, F$ are the midpoints of $BC, CA$ and $AB$ respectively. Find $DE,$ if $AB = 8 \ cm$
View full solution →In the given figure, $T$ is the midpoint of $QR$. Side $PR$ of $\triangle PQR$ is extended to $S$ such that $R$ divides $PS$ in the ratio $2:1$. $TV$ and $WR$ are drawn parallel to $PQ$. Prove that $T$ divides $SU$ in the ratio $2:1$ and $WR = \frac{1}{4} PQ$.
View full solution →In the given figure $, PS = 3RS. M$ is the midpoint of $QR$. If $TR \| MN \| QP,$ then prove that:
$ST =\frac{1}{3} LS$
View full solution →$ST =\frac{1}{3} LS$
In the given figure, the lines $l, m$ and $n$ are parallel to each other. $D$ is the midpoint of $CE$. Find: $a. BC, b. EF, c. CG$ and $d. BD.$
View full solution →In $\triangle ABC, D$ and $E$ are two points on the side $AB$ such that $AD = DE = EB$. Through $D$ and $E,$ lines are drawn parallel to $BC$ which meet the side $AC$ at points $F$ and $G$ respectively. Through $F$ and $G$, lines are drawn parallel to $AB$ which meet the side $BC$ at points $M$ and $N$ respectively.Prove that $BM = MN = NC.$
View full solution →In $\triangle ABC,$ the medians $BE$ and $CD$ are produced to the points $P$ and $Q$ respectively such that $BE = EP$ and $CD = DQ$. Prove that: $A$ is the mid$-$point of $PQ.$
View full solution →In $\triangle ABC, D$ and $E$ are the midpoints of the sides $AB$ and $AC$ respectively. $F$ is any point on the side $BC$. If $DE$ intersects $AF$ at $P$ show that $DP = PE$.
View full solution →The diagonals $AC$ and $BD$ of a quadrilateral $\text{ABCD}$ intersect at right angles. Prove that the quadrilateral formed by joining the midpoints of quadrilateral $\text{ABCD}$ is a rectangle.
View full solution →In $\triangle ABC$, the medians $BE$ and $CD$ are produced to the points $P$ and $Q$ respectively such that $BE = EP$ and $CD = DQ$. Prove that: $QA$ and $P$ are collinear.
View full solution →Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.
In $\triangle ABC, BE$ and $CF$ are medians. $P$ is a point on $BE$ produced such that $BE = EP$ and $Q$ is a point on $CF$ produced such that $CF = FQ$. Prove that : $A$ is the mid $-$ point of $PQ$.
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