Question

Similar Triangles 211 TRY THIS 1. Are triangles formed in each figure similar? Ifso, name the criterion of similarity. Write the similarity relation in symbolic form. (1) () 31 H M R 'K 10 (ii) 2 2 (iv) 3 AY X 3 5 w 3 В. C C (v) (vi) 400 600 B 800 B460° 809c 40° Р Р A cm. 70° 5 cm. (vii ) (viii 6 ст. . 70° R 5 cm. 2 cm. Qocm. 3 cm. 6 cm. R B B 2 cm. 4 cm. B4 C


plz.. answer the iv one fastly​

Answer 1

Step-by-step explanation:

(i) Yes, by AA criteria FGH~KIH

(ii) Not similar

(iii) Yes, by SAS criteria AXY~ABC

(iv) Not similar

(v) Yes, by AA criteria AOQ~BOP

(vi) sry but picture is not full

(vii) Not similar

(viii) Not similar

Answer 2

Answer:

(iv) the triangles are similar.

Step-by-step explanation:

(i) From ΔFGH and ΔHIK

•    ∠H = ∠H (opposite angles)    
•    ∠I = ∠G   (as IK and FG are parallel and IG is transversal)

So, from AA criterion for similarity of triangles

           ΔFGH similar to ΔHIK

(ii) From ΔPQR and ΔMNL

• ∠Q = ∠M = 90°
• But  $\frac{PQ}{LM}\neq \frac{QR}{MN}$  i.e.  $\frac{6}{3}\neq \frac{10}{4}$

So, ΔPQR is not similar to ΔMNL

(iii) From ΔAXY and ΔABC

• ∠A = ∠A (common angle)
• $\frac{AX}{AB} = \frac{AY}{AC} = (\frac{2}{5} = \frac{2}{5} )$

So, ΔAXY is similar to ΔABC

(iv) From ΔAPJ and ΔABC

• ∠A = ∠A (common angle)
• $\frac{AP}{AB} = \frac{AJ}{AC}$  $=(\frac{3}{8} = \frac{2}{\frac{16}{3} }=\frac{3}{8})$

So, ΔAPJ is similar to ΔABC

(v) From ΔOAQ and ΔOPB

• ∠O = ∠O (common angle)
• ∠A = ∠B = 90° (Given)

So, ΔOAQ is similar to ΔOPB

(vi) The picture is not clear!!, but you can do it yourself now from above              conclusions

(vii) From ΔABC and ΔPQR

• $(\frac{AB}{PQ}=\frac{2}{5} )\neq (\frac{BC}{QR}=\frac{2}{4} )$

So, ΔABC is not similar to ΔPQR

(viii) From ΔABC and ΔPQR

• ∠A = ∠P (Given)
• $(\frac{AB}{PQ}= \frac{6}{2.5} )\neq (\frac{AC}{PR}= \frac{10}{5} )$

So, ΔABC is not similar to ΔPQR

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