In pair of triangle in the following figure, parts bearing identical marks are congruent. State the test and correspondence if vertices by which triangle in each pair are congruent.

Question

In pair of triangle in the following figure, parts bearing identical marks are congruent. State the test and correspondence if vertices by which triangle in each pair are congruent.

Answer 1

In $Δ G H E$ and $Δ G F E$
$G H = E F G E = G E H E = G F$
So by $S S S$ criteria
The triangles are congruent.

Answer 2

In

Δ G H E

and

Δ G F E

G H = E F G E = G E H E = G F

So by

S S S

criteria

The triangles are congruent.

In pair of triangle in the following figure, parts bearing identical marks are congruent. State the test and correspondence if vertices by which triangle in each pair are congruent.

Answer

In $Δ G H E$ and $Δ G F E$
$G H = E F G E = G E H E = G F$
So by $S S S$ criteria
The triangles are congruent.

Related questions

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State whether the above statement is true or false.

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Hence $Δ B E C ≅ Δ D C F$ .
State whether the above statement is true or false.

$A B D F$ is a square and $B C = E F$ in the given figure. Prove that
i) $Δ A B C ≅ Δ A F E$
ii) $Δ A C G ≅ Δ A E G$

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, AP is bisector of $∠ A$ and CQ is bisector of $∠ C$ of parallelogram ABCD.
Prove that APCQ is a parallelogram

The following figure shows a triangle $A B C$ in which $A B = A C . M$ is a point on $A B$ and $N$ is a point on $A C$ , such that $B M = C N$ .
Prove that :
$A M = A N$
$Δ A M C ≅ Δ A N B$
$B N = C M$
$Δ B M C ≅ Δ C N B$

In given fig., $A D = B C$ and $∠ B A D = ∠ A B C$ , then $∠ A C B$ equals :

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In pair of triangle in the following figure, parts bearing identical marks are congruent. State the test and correspondence if vertices by which triangle in each pair are congruent.

Answer

In ΔGHE and ΔGFEGH=EFGE=GEHE=GFSo by SSS criteria The triangles are congruent.

Related questions

In the above figure Δ ABD ≅ Δ ACD,If ∠BDC = 1100 and ∠DAC = 300 then the measure of angle DBA is:

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ΔABC and ΔDBC are two isosceles triangle on the same base BC and vertices A and D are on the same side of BC (see fig7.39). If AD is extended to intersect BC at P, show that (i) ΔABD≅ΔACD (ii) ΔABP≅ΔACP (ii) AP bisects ∠A as wll as ∠D. (Iv) AP is the perpendicular bisector of BC.

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, AP is bisector of ∠A and CQ is bisector of ∠C of parallelogram ABCD. Prove that APCQ is a parallelogram

The following 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. Prove that : AM=AN ΔAMC≅ΔANB BN=CM ΔBMC≅ΔCNB

In given fig., AD=BC and ∠BAD=∠ABC, then ∠ACB equals :

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In $Δ G H E$ and $Δ G F E$
$G H = E F G E = G E H E = G F$
So by $S S S$ criteria
The triangles are congruent.

In the above figure $Δ$ ABD $≅$ $Δ$ ACD,If $∠$ BDC = $11 0^{0}$ and $∠$ DAC = $3 0^{0}$ then the measure of angle DBA is:

Quadrilateral ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Hence, $Δ A D X ≅ Δ B A Y$
State whether the above statement is true or false.

In $Δ A B C, A B = A C$ and $A D$ is perpendicular bisector of $B C$ . The property by which $Δ A D B$ is not congruent to $Δ A D C$ is ______________.

ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that AB = BE and AD = DF.
Hence $Δ B E C ≅ Δ D C F$ .
State whether the above statement is true or false.

$A B D F$ is a square and $B C = E F$ in the given figure. Prove that
i) $Δ A B C ≅ Δ A F E$
ii) $Δ A C G ≅ Δ A E G$

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, AP is bisector of $∠ A$ and CQ is bisector of $∠ C$ of parallelogram ABCD.
Prove that APCQ is a parallelogram

The following figure shows a triangle $A B C$ in which $A B = A C . M$ is a point on $A B$ and $N$ is a point on $A C$ , such that $B M = C N$ .
Prove that :
$A M = A N$
$Δ A M C ≅ Δ A N B$
$B N = C M$
$Δ B M C ≅ Δ C N B$

In given fig., $A D = B C$ and $∠ B A D = ∠ A B C$ , then $∠ A C B$ equals :