In D E F and - P Q R- it is given that - D- Q and - R- E- then which of the following is not true-a EFPR-DFPQb DEPQ-EFRPc DEQR -DFPQd EFRP-DEQR

(b) DEPQ #160;= #160;EFRP In ∆DEF and ∆PQR, we have: #8736;D #160;= #160; #8736;Q #160;and #160; #8736;R #160;= #160; #8736;EApplyin ...

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Byju's Answer

Standard X

Mathematics

AAA Similarity

In D E F and ...

Question

In ∆DEF and ∆PQR, it is given that ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?
(a) $\frac{E F}{P R} = \frac{D F}{P Q}$
(b) $\frac{D E}{P Q} = \frac{E F}{R P}$
(c) $\frac{D E}{Q R} = \frac{D F}{P Q}$
(d) $\frac{E F}{R P} = \frac{D E}{Q R}$

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Solution

(b) $\frac{D E}{P Q} = \frac{E F}{R P}$

In ∆DEF and ∆PQR, we have:

$∠ D = ∠ Q and ∠ R = ∠ E Applying A A similarity theorem, we conclude that △ D E F ~ △ Q R P . Hence, \frac{D E}{Q R} = \frac{D F}{Q P} = \frac{E F}{P R}$

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Similar questions

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}

Q. If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then

\frac{D E}{Q R} = \frac{D F}{P Q}

= _________.

Q. Question 6
If in two

Δ D E F a n d Δ P Q R, ∠ D = ∠ Q a n d ∠ R = ∠ E

, then which of the following is not true?

(A)

\frac{E F}{P R} = \frac{D F}{P Q}

(B)

\frac{D E}{P Q} = \frac{E F}{R P}

(C)

\frac{D E}{Q R} = \frac{D F}{P Q}

(D)

\frac{E F}{R P} = \frac{D E}{Q R}

Q. If in two triangles

D E F

and

P Q R

∠ D = ∠ Q

and

∠ R = ∠ E

, then which of the following is not true?

Q. Question 6
If in two

Δ D E F a n d Δ P Q R, ∠ D = ∠ Q a n d ∠ R = ∠ E

, then which of the following is not true?

(A)

\frac{E F}{P R} = \frac{D F}{P Q}

(B)

\frac{D E}{P Q} = \frac{E F}{R P}

(C)

\frac{D E}{Q R} = \frac{D F}{P Q}

(D)

\frac{E F}{R P} = \frac{D E}{Q R}

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In ∆DEF and ∆PQR, it is given that ∠D = ∠Q and ∠R = ∠E, then which of the following is not true? (a) EFPR=DFPQ (b) DEPQ=EFRP (c) DEQR=DFPQ (d) EFRP=DEQR

(b) DEPQ = EFRP In ∆DEF and ∆PQR, we have: ∠D = ∠Q and ∠R = ∠EApplying AA similarity theorem, we conclude that △DEF~△QRP.Hence, DEQR = DFQP = EFPR

In ∆DEF and ∆PQR, it is given that ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?
(a) $\frac{E F}{P R} = \frac{D F}{P Q}$
(b) $\frac{D E}{P Q} = \frac{E F}{R P}$
(c) $\frac{D E}{Q R} = \frac{D F}{P Q}$
(d) $\frac{E F}{R P} = \frac{D E}{Q R}$

(b) $\frac{D E}{P Q} = \frac{E F}{R P}$

In ∆DEF and ∆PQR, we have:

$∠ D = ∠ Q and ∠ R = ∠ E Applying A A similarity theorem, we conclude that △ D E F ~ △ Q R P . Hence, \frac{D E}{Q R} = \frac{D F}{Q P} = \frac{E F}{P R}$