Which of the following pairs of triangles are congruent In each case state the condition of congruency a In ABC and DEF ABDE BCEF and BE b In ABC and DEF BE 90 ACDF and BCEF c In ABC and QRP ABQR BR and CP d In ABC and PQR ABPQ ACPR and BCQR e In ABC and PQR BCQR A90 CR40o and Q50

Selina Solutions Class 9 Mathematics Solutions for Exercise 9(A) in Chapter 9 - Chapter 9- Triangles [Congruency in Triangles]

Question 1 Exercise 9(A)

Which of the following pairs of triangles are congruent? In each case, state the

condition of congruency:

(a) In 𝚫 ABC and 𝚫 DEF, AB=DE, BC=EF and ∠B=∠E.

(b) In 𝚫 ABC and 𝚫 DEF, ∠B=∠E = 90° ; AC=DF and BC=EF.

(d) In 𝚫 ABC and 𝚫 PQR, AB=PQ, AC=PR, and BC=QR.

(e) In 𝚫 ABC and 𝚫 PQR, BC=QR, ∠A=90°, ∠C=∠R=40o and ∠Q=50°.

Answer:

Solution:

Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 9- Triangles [Congruency in Triangles] Question 1 Solution image

Video transcript

"hello students my name is rabbit singh and i welcome you all to lido learning homework one of india's best online classes now today in this video we have a question that is based on the topic of congruent triangles the question says basically we have five questions parts in which we have to tell which criteria will be following in order to prove the two triangles congruent now which of the following pairs of triangles are congruent in each case state the conditions of congruency now first part in triangle abc and triangle d e f a b is equal to d that means side bc is equal to e f that means side and angle b central angle will be equal to angle e so triangle abc will be congruent to triangle def by side angle side criterion that is sas criterion similarly for the second one in triangle abc and triangle def angle b and angle e are 90 degree that means angle ac is equal to df so that means side and bc is equal to ef that means again side so this criterion is also sas triangle abc and triangle def are congruent based on ss criterion third in triangle abc and triangle qrp a b is equal to qr that is side angle b is equal to angle r that is angle and angle c is equal to angle p so that is again angle so based on aas criterion triangle abc is congruent to triangle qrp now second last in triangle abc and triangle pq are a b is equal to pq that means first side ac is equal to pr that means second side and bc is equal to qr that means third side so all the three sides that means triple s criterion triangle abc is congruent to triangle pqr last in triangle abc and triangle pqr bc is equal to qr first side angle a is equal to 90 degree and angle q is equal to 50 degree so an angle c and r are 40 degree so first side are equal and second angle are equal and angle a is 90 and angle c and angle are okay so let us make the figure for this question this is triangle abc in which angle a sorry this is a this is b and this is c because angle a is given 90 degree so angle a is 90 degree similarly in the second figure angle q is given an angle r is given so angle q is 50 degrees so this is q that is 50 degrees p is 90 degrees and pqr r is given 40 degrees now if we check based on this a is 50 is 90 b is 90 so that is given angle c is equal to angular 40 degrees that is already given angle c is equal to angular 40 degrees that is already given an angle q and angle b are 50 degrees so based on aas criterion triangle abc is congruent to triangle pqr based on this figure so i hope you have understood the concept very clearly but still if you have any doubt do comment in the comment box and please like and subscribe our channel follow thank you"

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