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(a) In the adjoining figure, it is given that AB=3y. AC=7x. AD=9x and AE=13+2y. Find the values of x and y. [3]

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In the given figure $A B = B D$ and $∠ B A C = ∠ D A C$ . Is $△ A B C \equiv △ A D C$ ?
If so, state the other pairs of corresponding parts.

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The given figure shows a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Hence,AM = AN

State true or false.

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PR = AB
State whether the above statement is true or false.

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State the congruency of following pairs of triangles.
In $Δ A B C$ and $Δ P Q R$ , $B C = Q R,$ $∠ A = 9 0^{\circ}, ∠ C = ∠ R = 4 0^{\circ}$ and $∠ Q = 5 0^{\circ}$ .

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In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively. Hence, BQ = CP.
State whether the above statement is true or false.

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In the given figure, $A P$ bisects $∠ A$ , and $A B$ = $A C$ .
Is $B P$ > $P Q$ .

View solution

If the medians of a triangle $A B C$ intersect at $G,$ prove that:
$a r . (Δ A G B) = a r . (Δ A G C) = a r (Δ B G C) = \frac{1}{3} a r (Δ A B C)$

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In the given figure, two sides $A B$ and $B C$ and the median $A D$ drawn to side $B C$ of $△ A B C$ are equal to the two sides $P Q$ and $Q R$ and the corresponding median $P M$ of the other $△ P Q R .$ Which of the following is not correct $?$

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$Δ A B C \sim Δ D E F$ , $(Δ A B C)$ : $(Δ D E F)$ $=$ ?

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In a squared sheet, draw two triangles of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent
What can you say about their perimeters?

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(a) In the adjoining figure, it is given that AB=3y. AC=7x. AD=9x and AE=13+2y. Find the values of x and y. [3]

Answer

Related questions

In the given figure $A B = B D$ and $∠ B A C = ∠ D A C$ . Is $△ A B C \equiv △ A D C$ ?
If so, state the other pairs of corresponding parts.

The given figure shows a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Hence,AM = AN

State true or false.

PR = AB
State whether the above statement is true or false.

State the congruency of following pairs of triangles.
In $Δ A B C$ and $Δ P Q R$ , $B C = Q R,$ $∠ A = 9 0^{\circ}, ∠ C = ∠ R = 4 0^{\circ}$ and $∠ Q = 5 0^{\circ}$ .

In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively. Hence, BQ = CP.
State whether the above statement is true or false.

In the given figure, $A P$ bisects $∠ A$ , and $A B$ = $A C$ .
Is $B P$ > $P Q$ .

If the medians of a triangle $A B C$ intersect at $G,$ prove that:
$a r . (Δ A G B) = a r . (Δ A G C) = a r (Δ B G C) = \frac{1}{3} a r (Δ A B C)$

In the given figure, two sides $A B$ and $B C$ and the median $A D$ drawn to side $B C$ of $△ A B C$ are equal to the two sides $P Q$ and $Q R$ and the corresponding median $P M$ of the other $△ P Q R .$ Which of the following is not correct $?$

$Δ A B C \sim Δ D E F$ , $(Δ A B C)$ : $(Δ D E F)$ $=$ ?

In a squared sheet, draw two triangles of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent
What can you say about their perimeters?

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(a) In the adjoining figure, it is given that AB=3y. AC=7x. AD=9x and AE=13+2y. Find the values of x and y. [3]

Answer

Related questions

In the given figure AB=BD and ∠BAC=∠DAC. Is △ABC≡△ADC? If so, state the other pairs of corresponding parts.

The given figure shows a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.Hence,AM = AN State true or false.

PR = AB State whether the above statement is true or false.

State the congruency of following pairs of triangles.In ΔABC and ΔPQR, BC=QR, ∠A=90∘,∠C=∠R=40∘ and ∠Q=50∘.

In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively. Hence, BQ = CP.State whether the above statement is true or false.

In the given figure, AP bisects ∠A, and AB = AC. Is BP>PQ .

If the medians of a triangle ABC intersect at G, prove that: ar.(ΔAGB)=ar.(ΔAGC)=ar(ΔBGC)=31​ar(ΔABC)

In the given figure, two sides AB and BC and the median AD drawn to side BC of △ABC are equal to the two sides PQ and QR and the corresponding median PM of the other △PQR. Which of the following is not correct?

ΔABC∼ΔDEF, (ΔABC) : (ΔDEF) = ?

In a squared sheet, draw two triangles of equal areas such that (i) the triangles are congruent. (ii) the triangles are not congruent What can you say about their perimeters?

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Take Toppr Scholastic Test for Aptitude and Reasoning

Win exciting scholarships and plan a great education plan

In the given figure $A B = B D$ and $∠ B A C = ∠ D A C$ . Is $△ A B C \equiv △ A D C$ ?
If so, state the other pairs of corresponding parts.

The given figure shows a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Hence,AM = AN

State true or false.

PR = AB
State whether the above statement is true or false.

State the congruency of following pairs of triangles.
In $Δ A B C$ and $Δ P Q R$ , $B C = Q R,$ $∠ A = 9 0^{\circ}, ∠ C = ∠ R = 4 0^{\circ}$ and $∠ Q = 5 0^{\circ}$ .

In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively. Hence, BQ = CP.
State whether the above statement is true or false.

In the given figure, $A P$ bisects $∠ A$ , and $A B$ = $A C$ .
Is $B P$ > $P Q$ .

If the medians of a triangle $A B C$ intersect at $G,$ prove that:
$a r . (Δ A G B) = a r . (Δ A G C) = a r (Δ B G C) = \frac{1}{3} a r (Δ A B C)$

In the given figure, two sides $A B$ and $B C$ and the median $A D$ drawn to side $B C$ of $△ A B C$ are equal to the two sides $P Q$ and $Q R$ and the corresponding median $P M$ of the other $△ P Q R .$ Which of the following is not correct $?$

$Δ A B C \sim Δ D E F$ , $(Δ A B C)$ : $(Δ D E F)$ $=$ ?

In a squared sheet, draw two triangles of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent
What can you say about their perimeters?