Medians of a Triangle and the Drawing Method

Q.

Let the orthocentre and centroid of a triangle be $A\left(-3,5\right)$ and $B\left(3,3\right)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is

1. $3\sqrt{\frac{5}{2}}$

2. $\frac{3\sqrt{5}}{2}$

3. $\sqrt{10}$

4. $2\sqrt{10}$

Q.

If a $∆ABC$ has vertices$(0,0),(11,60)$ and $(91,0)$. If the line $y=kx$ cuts the triangle into two triangles of equal area, then $k$is equal to

1. $\frac{30}{51}$

2. $\frac{4}{7}$

3. $\frac{7}{4}$

4. $\frac{30}{91}$

Q. In triangle ABC AD is the median, then which of the following is correct ?

1. BD = 2CD
2. BD = CD
3. AD = AC
4. AB = BD

Q.

In $△$ABC, AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$DEF is similar to $△$ABC. If EF = 4 cm, then the perimeter of $△$DEF is -

1. 7.5 cm

2. 15 cm

3. 22.5 cm

4. 30 cm

Q. Three Angeles of quadrilateral is are in ratio 3:5:8. The mean of these three angles is 80°. Find all the angles

Q. Which among the following is true for a triangle?

1. A median is line joining the vertex to the midpoint of the opposite side.
2. A median always lies outside the triangle.
3. A centroid always lies outside the triangle.
4. The point of intersection of medians is known as orthocentre.

Q.

Question 7 (i)
In a squared sheet, draw two triangles of equal area such that:
The triangles are congruent.
What can you say about their perimeters?

Q. Question 3 (i)
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:
$\Delta ABM\cong \Delta PQN$

Q. In the figure below, if D is the mid point of BC, then the line AD is called as __________.

1. Median
2. Mode
3. Middle line
4. centroid

Q.

You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for $\Delta ABC$ whose vertices are $A(4,-6),B(3,-2)\mathrm{and}C(5,2).$

Q. In the given equilateral triangle ABC, AP is the median in triangle ABC. Find the value of angle PAC.

1. ${30}^{\circ }$
2. ${75}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. In an equilateral triangle ABC, AD, BE and CF are the medians. If the length of AB = 7 cm, find the length of CE.

1. 3 cm
2. 3.5 cm
3. 6.5 cm
4. 7 cm

Q. What is the total number of medians that a triangle can have?

1. 1
2. 2
3. 3
4. 4

Q. Which triangle has its altitude as its median?

1. Equilateral triangle
2. Right angled triangle
3. Obtuse angled triangle
4. Actue angled triangle

Q.

Three angles of a quadrilateral are in the ratio 2:3:7. The mean of these angles is 64°. Find all the angles

Q.

Draw a rough sketch of triangle DEF. Draw all medians of triangle DEF. Mark its centroid as G.

Q.

A line, $AB$ of $4cm$ is drawn. Another line, $CD$ which is congruent and perpendicular to $AB$ is drawn. Length of $CD$ is

1. 5 cm
2. 4 cm
3. Can't say
4. 3 cm

Q. In the figure AD = EC, which additional information is needed to show that $△ABD$ and $△EBC$ will be congruent by A - A - S test?

1. $DB=EB$
2. $\angle BAD=\angle BEC$
3. $\angle BAD={40}^o$
4. $AB=CB$

Q. Vertices of a $△$ABC are A (2, 2), B (-4, -4)and C (5, -8), then the length of the median through C is :

1. $\sqrt{65}$
2. $\sqrt{117}$
3. $\sqrt{85}$
4. $\sqrt{113}$

Q. Origin is the centre of circle passing through the vertices of an equilateral triangle whose median is of length $3a$ then equation of the circle is?

1. $x^2+y^2=a^2$
2. $x^2+y^2=2a^2$
3. $x^2+y^2=3a^2$
4. $x^2+y^2+4a^2$

Q.
In the given triangle PQR, D is the mid point of side QR then what is PM and PD?

1. Median and altitude
2. Altitude and median
3. Angle bisector and altitude
4. Angle bisector and median

Q. In a triangle, the line segment joining a vertex to the midpoint of the opposite side is called as .

1. altitude
2. median
3. angle bisector

Q.

If AM is a median of triangle ABC. Then AB +BC +CA $>$ 2AM

1. AB+BC+CA = 2 AM

2. AB+BC+CA > 2AM

Q. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure).
Is $\Delta ABM\cong \Delta PQN$?

1. Yes
2. No

Q. Construct a $△ABC$ in which the base $BC=5$ cm, $\angle BAC={40}^{\circ }$ and the median from $A$ to $BC$ is $6$ cm. Also measure the length of the altitude from $A$.

Q. If $AD,BE$ and $CF$ are the medians of a $△ABC$, then $(A{D}^2+B{E}^2+C{F}^2):(B{C}^2+C{A}^2+A{B}^2)$ is equal to

1. $3:4$
2. $2:3$
3. Minimum value of $\frac{3}{8}({\tan }^2\theta +{\cot }^2\theta )$
4. Minimum value of $\frac{1}{3}({\tan }^2\theta +{\cot }^2\theta )$

Q. The side of a triangle measures 8cm. The median divides the side into ___ and ___ .

1. 4 cm and 4 cm
2. 2 cm and 6 cm
3. 6 cm and 2 cm
4. 5 cm and 3 cm

Q. In $\Delta ABC$, AD is median of $\Delta ABC$ and BE is median of $\Delta ABD$.

1. 60 $c{m}^2$
2. 50 $c{m}^2$
3. 40 $c{m}^2$
4. 30 $c{m}^2$

Q. If G is centroid and AD, BE, CF are three medians of ABC with area 72 $c{m}^2$ , then the area of BDG is

1. 12 $c{m}^2$
2. 8 $c{m}^2$
3. 24 $c{m}^2$
4. 16 $c{m}^2$

Q.

Which of the following is incorrect?

1. Sum of the three sides of a triangle is less than the sum of its three medians

2. The sum of any two sides of a triangle is always greater than the third side

3. Sum of any two sides of a triangle is greater than twice the median drawn to the third side

4. If two angles of a triangle are unequal, then the greater angle has the greater side opposite to it