If two medians of a triangle are equal, then the triangle is

Question

If two medians of a triangle are equal, then the triangle is

Answer 1

If $B E = C F$ and G is centroid, then
$G C = \frac{2}{3} F C = \frac{2}{3} B E = B G$
$F G = \frac{1}{3} F C = \frac{1}{3} B E = E G$
$∠ G = ∠ G$
$∴ Δ F G B ≅ Δ E G C$ (By SAS postulate)
$∴ F B = E C$
$o r \frac{1}{2} A B = \frac{1}{2} A C o r A B = A C$
Therefore, $Δ A B C$ is isosceles.

Answer 2

If

B E = C F

and G is centroid, then

G C = \frac{2}{3} F C = \frac{2}{3} B E = B G

F G = \frac{1}{3} F C = \frac{1}{3} B E = E G

∠ G = ∠ G

∴ Δ F G B ≅ Δ E G C

(By SAS postulate)

∴ F B = E C

o r \frac{1}{2} A B = \frac{1}{2} A C o r A B = A C

Therefore,

Δ A B C

is isosceles.

If two medians of a triangle are equal, then the triangle is

Equilateral

Isosceles

Scalene

Right-angled

Answer

Practice important Questions

NTSE Maths Volume II Chapter 11 to 13

Related questions

In $Δ A B C$ and $Δ P Q R, ∠ A = ∠ Q$ and $∠ B = ∠ R$ which side of $Δ P Q R$ should be equal to the side $A B$ of $Δ A B C$ , so two triangles become congruent. Give reason to your answer.

Referring to the given figure, $E$ is the center of the circle and $A C$ and $B D$ are diameters. If $Δ A E B ≅ Δ D E C$ , then the congruence theorem used to prove this is:

In $△ A B C$ , $∠ A B C = 9 0^{0}$ , $B D ⊥ A C$ . If $B D = 8 c m, A D = 4 c m .$ Find $C D$ and $A B .$

Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN.
BMDN is a __________.

In the adjacent figure, $C D$ and $B E$ are altitudes of an isosceles triangle $A B C$ with $A C = A B$ . Prove that $A E = A D$

$△$ ABC and $△$ DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions given; AB = DE, AC =DF, $∠$ ABC = $∠$ DEF are

State, whether the pairs of triangles given in the following figures are congruent or not:

Which of the following statements is INCORRECT?

Without drawing the triangles write all size pairs of equal measures in each of the following pairs of congruent triangles.
$△ X Y Z ≅ △ M L N$

In the figure $B C = 2$ then $D E =$ ____.

Learn with content

Take Toppr Scholastic Test for Aptitude and Reasoning

Win exciting scholarships and plan a great education plan

If two medians of a triangle are equal, then the triangle is

Equilateral

Isosceles

Scalene

Right-angled

Answer

If BE=CF and G is centroid, then GC=32​FC=32​BE=BG FG=31​FC=31​BE=EG ∠G=∠G ∴ΔFGB≅ΔEGC (By SAS postulate) ∴FB=EC or21​AB=21​ACorAB=AC Therefore, ΔABC is isosceles.

Practice important Questions

NTSE Maths Volume II Chapter 11 to 13

Related questions

In ΔABC and ΔPQR,∠A=∠Q and ∠B=∠R which side of ΔPQR should be equal to the side AB of ΔABC, so two triangles become congruent. Give reason to your answer.

Referring to the given figure, E is the center of the circle and AC and BD are diameters. If ΔAEB≅ΔDEC, then the congruence theorem used to prove this is:

In △ABC, ∠ABC=900, BD⊥AC. If BD=8 cm,AD=4 cm. Find CD and AB.

Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN. BMDN is a __________.

In the adjacent figure, CD and BE are altitudes of an isosceles triangle ABC with AC=AB. Prove that AE=AD

△ ABC and △ DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions given; AB = DE, AC =DF, ∠ ABC = ∠ DEF are

State, whether the pairs of triangles given in the following figures are congruent or not:

Which of the following statements is INCORRECT?

Without drawing the triangles write all size pairs of equal measures in each of the following pairs of congruent triangles. △XYZ≅△MLN

In the figure BC=2 then DE=____.

Learn with content

Take Toppr Scholastic Test for Aptitude and Reasoning

Win exciting scholarships and plan a great education plan

In $Δ A B C$ and $Δ P Q R, ∠ A = ∠ Q$ and $∠ B = ∠ R$ which side of $Δ P Q R$ should be equal to the side $A B$ of $Δ A B C$ , so two triangles become congruent. Give reason to your answer.

Referring to the given figure, $E$ is the center of the circle and $A C$ and $B D$ are diameters. If $Δ A E B ≅ Δ D E C$ , then the congruence theorem used to prove this is:

In $△ A B C$ , $∠ A B C = 9 0^{0}$ , $B D ⊥ A C$ . If $B D = 8 c m, A D = 4 c m .$ Find $C D$ and $A B .$

Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN.
BMDN is a __________.

In the adjacent figure, $C D$ and $B E$ are altitudes of an isosceles triangle $A B C$ with $A C = A B$ . Prove that $A E = A D$

$△$ ABC and $△$ DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions given; AB = DE, AC =DF, $∠$ ABC = $∠$ DEF are

Without drawing the triangles write all size pairs of equal measures in each of the following pairs of congruent triangles.
$△ X Y Z ≅ △ M L N$

In the figure $B C = 2$ then $D E =$ ____.