Median of Triangle

Q.

A man and his wife appear for an interview for two vacancies in the same posts. The probability of the husband’s selection is 1/7 and that of the wife’s selection is 1/5. What is the probability that only one of them will be selected

1. $\frac{1}{7}$

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

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

4. None of these

Q.

If $a,bandcareinA.P$, then $\frac{{(a-c)}^2}{b^2-ac}$is

1. $1$

2. $2$

3. $3$

4. $4$

Q.

A man and woman appear in an interview for two vacancies in the same post. The probability of the man’s selection is ¼ and that of the woman’s selection is 1/3. What is the probability that none of them will be selected

1. $\frac{1}{2}$

2. $\frac{1}{12}$

3. $\frac{1}{4}$

4. None of these

Q.

If A (5, –1), B(–3, –2) and C(–1, 8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.

Q.

A __ connects a vertex of a triangle to the midpoint of the opposite side.

Q.

If $a,b,c$are in G.P then

Q.

The point of intersection of medians is known as centroid. The centroid divides the median in the ratio________.

1. Incentre

2. Orthocentre

3. Centroid

4. Circumcentre

Q.

A median of a scalene triangle is a line segment joining a vertex to the ___ of the opposite side.

1. midpoint

2. incenter

3. orthocenter
4. circumcenter

Q. The ratio that centroid divides the median is ______.

1. 7:2
2. 3:5
3. 7:9
4. 2:1

Q.

According to the construction shown in the diagram below, what do we call segment CD?

1. Median to side AB

2. Perpendicular bisector of segment AB

3. Bisector of angle C

4. Altitude to side AB

Q.

$~(p\vee q)\vee (~p\wedge q)$is logically equivalent to

1. $~p$

2. $p$

3. $q$

4. $~q$

Q. Is a line drawn from a vertex and bisect the opposite side?

Q.

$BD$ is a median of a triangle $ABC$. $F$ is a point on $AB$ such that $CF$ intersects $BDatE$ and $BE=ED$. If $BF=5cm$, $BA$ is equal to

1. $10$

2. $12$

3. $15$

4. $17$

Q. Question 5
Determine, algebraically, the vertices of the triangle formed by the lines
3x – y = 3
2x – 3y = 2
x + 2y = 8

Q.

For a scalene triangle if the sides of a triangle is given but height is not given, how will the area of that triangle be calculated?

Q.

In the given figure, AF is parallel to CD, ED is parallel to FC and AD is parallel to BI. J is the mid point of AI. What will be the ratio of $\frac{\text{Area of trapezium AJCB}}{\text{Area of parallelogram EFCD}}$?

1. $1$

2. $\frac{1}{2}$

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

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

Q.

If A (-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle. Median through(-1, 8) intersect line segment BC at D. Find the co-ordinates of point D.

1. 

2. 

3. 

4. 

Q. ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.

Q.

The point of intersection of medians is called___ .

Q. ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF =

(a) AE

(b) BE

(c) CE

(d) DE

Q.

Diagonals of a parallelogram divide it into four triangles of equal area

1. False

2. True

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

In the given figure, BF, BD and CE, CD are the exterior angle bisectors of ∠B and ∠C respectively, BE and CF are the interior angle bisectors of ∠B and ∠C respectively. If α + θ = 130° and ∠B – ∠C = 20°, then which of the following option(s) is/are correct?

दिए गए चित्र में BF, BD तथा CE, CD क्रमशः ∠B व ∠C के बाह्य कोण समद्विभाजक हैं, BE व CF क्रमशः ∠B व ∠C के अन्तः कोण समद्विभाजक हैं। यदि α + θ = 130° तथा ∠B – ∠C = 20°, तब निम्न में से कौनसा/कौनसे विकल्प सही है/हैं?

1. β = 20°
   
2. γ = θ – δ
   
3. θ = α + β + γ
   
4. $\angle C=\frac{1}{4}\left(\angle A+\angle B\right)$
   

Q. Write the ratio in which centroid of triangle divide the median.

Q. An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

Q. If the length of median $A{A}_1,B{B}_1$ and $C{C}_1$ of triangle ABC are $m_a,m_b$ and $m_c$ respectively. Then

1. $\sum ma>\frac{3}{2}s$
2. $\sum ma>3s$
3. $\sum ma>\frac{5}{2}s$
4. $\sum ma>2s$

Q. Construct a triangle $ABC$ in which $AB=4.5cm$, $AC=5.5cm$ and the median $AD=4cm$.

Q. The vertices of $△ABC$ are $A(2,1),B(-2,3)$ and $C(4,5)$. Find the equation of the median through the vertex $A$.

Q. Prove that the medians bisecting the equal sides of an isosceles triangle are equal.

Q. $O$ is any point inside rectangle $ABCD$. Prove that $O{B}^2+O{D}^2=O{A}^2+O{C}^2$.

Q. ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =

(a) 55°

(b) 70°

(c) 35°

(d) 110°