Tag: the mid-point theorem

Question 1

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

State true or false:

$ D, E $ and $ F $ are the mid-points of the sides $ AB, BC $ and $ CA $ of an isosceles $ \bigtriangleup ABC $ in which $ AB= BC $. then
$ \bigtriangleup DEF $ is also isosceles.

True
False

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Answer

$AE^2+CD^2=\frac {5}{4}AC^2$

Answer

$(-2a, 4b)$

Answer

$P-$ Median; $Q$- Altitude; $R-3$; $S-3$

Answer

area of $\Delta DEF=8$

Question 2

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

In $\Delta ABC$, D and E are mid points of AB and BC respectively and $\angle ABC=90^o$, then

$AE^2+CD^2=AC^2$
$AE^2+CD^2=\frac {3}{4}AC^2$
$AE^2+CD^2=\frac {4}{5}AC^2$

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Question 3

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

Find the midpoint of the segment connecting the points $(a, -b)$ and $(5a, 7b)$.

$(3a, -3b)$
$(2a, -3b)$
$(3a, -4b)$
none of these

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Question 4

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

Fill in the blanks:
(i) The ling segment joining a vertex of a triangle to the midpoint of its opposite side is called a $\underline { P } $ of the triangle.
(ii) The perpendicular line segment from a vertex of a triangle to its opposite is called an $\underline { Q } $ of the triangle
(iii) A triangle has $\underline { R } $ altitudes and $\underline { S } $ medians

$P-$ Altitude; $Q$- Median; $R-1$; $S-1$
$P-$ Altitude; $Q$- Median; $R-3$; $S-3$
$P-$ Median; $Q$- Altitude; $R-2$; $S-3$

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Question 5

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the _______ side.

first
second
third
none of the above

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Question 6

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

Fill in the blank:

Line joining the mid-points of any two sides of a triangle is _____ to the third side.

perpendicular
parallel
Inclined at $60^o$
None of these

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Question 7

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

If the lengths of the medians $AD, BE$ and $CF$ of the triangle $ABC$, are $6,8,10$ respectively, then

$AD$ and $BE$ are perpendicular
$BE$ and $CF$ are perpendicular
area of $\Delta ABC=32$

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Question 8

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

In $\triangle ABC , \angle B=90^0$ and D is the mid-point of BC then
$BC^2=4(AD^2-AB^2)$

True
False

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Question 9

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

The area of rectangle ABCD with vertices A (0,0), B (5,0), C (5, 6) and D (0,6) is

$25cm^2$
$20cm^2$
$30cm^2$
None of these.

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Question 10

Multiple choice maths mid-point and its converse proving the mid-point theorem the mid-point theorem mid point theorem

If a line cuts sides $BC, CA$ and $AB$ of $\triangle ABC$ at $P, Q, R$ respectively then " $\dfrac {BP}{PC}\cdot \dfrac {CQ}{QA}\cdot \dfrac {AR}{RB} = 1$. " that statement is ?

True
False

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