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Standard IX

Mathematics

Congruent Triangles

Given are two...

Question

Given are two congruent triangles $P Q R$ and $X Y Z$ . Which of the following statements is incorrect?

∠ Q = ∠ Y

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∠ P = ∠ X

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Δ P Q R ≅ Δ X Y Z

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Δ P Q R ≅ Δ Z X Y

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Solution

The correct option is D $Δ P Q R ≅ Δ Z X Y$
According to the given figure, $∠ P = ∠ X, ∠ R = ∠ Z$ , and $P R = Z X$ .

$∴ Δ P Q R ≅ Δ X Y Z$ .

$∠ Q = ∠ Y$ (angle sum property)

Hence, $Δ P Q R ≅ Δ Z X Y$ is an incorrect statement.

Therefore, option $D$ is correct.

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Similar questions

Q. For two triangles PQR and XYZ,

\frac{P Q}{Q R} = \frac{Y Z}{Z X}

and

\frac{Q R}{P R} = \frac{Z X}{Y X}

Q. ∆ PQR and ∆ XYZ such that l(PQ) = l(XY), l(QR) = l(YZ), l(RP) = l(ZX), then the triangles are congruent by

Q. In the given congruent triangles under ASA, find the value of x and y, ΔPQR

≅

ΔSTU.

Question 63

Fill in the blanks to make the statement true.

If $Δ P Q R$ and $Δ X Y Z$ are congruent under the correspondence $Q P R \leftrightarrow X Y Z$ , then
(i) $∠ R =$ ___ (ii) QR = ___
(iii) $∠ P =$ ___ (iv) QP = ___
(v) $∠ Q =$ ___ (v) RP = ___

Q. Select the appropriate alternative.
(1) In ∆ABC and ∆PQR, in a one to one correspondence

\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}

then

(A) ∆PQR ~ ∆ABC
(B) ∆PQR ~ ∆CAB
(C) ∆CBA ~ ∆PQR
(D) ∆BCA ~ ∆PQR

(2) If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false?

(A)

\frac{EF}{PR} = \frac{DF}{PQ}

(B)

\frac{DE}{PQ} = \frac{EF}{RP}

(C)

\frac{DE}{QR} = \frac{DF}{PQ}

(D)

\frac{EF}{RP} = \frac{DE}{QR}

(3) In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ?
(A)The triangles are not congruent and not similar
(B) The triangles are similar but not congruent.
(C) The triangles are congruent and similar.
(D) None of the statements above is true.

(4) ∆ABC and ∆DEF are equilateral triangles, A (∆ABC) : A (∆DEF) = 1 : 2
If AB = 4 then what is length of DE?
(A)

2 \sqrt{2}

(B) 4
(C) 8
(D)

4 \sqrt{2}

(5) In the given figure, seg XY || seg BC, then which of the following statements is true?

(A)

\frac{AB}{AC} = \frac{AX}{AY}

(B)

\frac{AX}{XB} = \frac{AY}{AC}

(C)

\frac{AX}{YC} = \frac{AY}{XB}

(D)

\frac{AB}{YC} = \frac{AC}{XB}

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Given are two congruent triangles PQR and XYZ. Which of the following statements is incorrect?

The correct option is D ΔPQR≅ΔZXYAccording to the given figure, ∠P=∠X,∠R=∠Z, and PR=ZX.∴ΔPQR≅ΔXYZ.∠Q=∠Y (angle sum property)Hence, ΔPQR≅ΔZXY is an incorrect statement.Therefore, option D is correct.

Given are two congruent triangles $P Q R$ and $X Y Z$ . Which of the following statements is incorrect?

The correct option is D $Δ P Q R ≅ Δ Z X Y$
According to the given figure, $∠ P = ∠ X, ∠ R = ∠ Z$ , and $P R = Z X$ .

$∴ Δ P Q R ≅ Δ X Y Z$ .

$∠ Q = ∠ Y$ (angle sum property)

Hence, $Δ P Q R ≅ Δ Z X Y$ is an incorrect statement.

Therefore, option $D$ is correct.