Question

Which triangles could not be similar to triangle ABC ? triangle a b c where angle b is a right angle. side a b is 15 cm. side b c is 8 cm. side a c is 17 cm. Select each correct answer. Right triangle G H I with right angle at H. G H is 77 centimeters. G I is 85 centimeters. H I is 36 centimeters. Right triangle J K L with right angle at K. J K is 60 centimeters. J L is 68 centimeters. K L is 32 centimeters. Right triangle M N O with right angle at N. M N is 35 centimeters. M O is 37 centimeters. N O is 12 centimeters. Right triangle D E F with right angle at E. D E is 22.5 centimeters. D F is 25.5 centimeters. E F is 12 centimeters.

Answer 1

Answer:

option (b) and (d) are correct.

 Right triangle J K L with right angle at K. J K is 60 centimeters. J L is 68 centimeters. K L is 32 centimeters.

and Right triangle D E F with right angle at E. D E is 22.5 centimeters. D F is 25.5 centimeters. E F is 12 centimeters.

Step-by-step explanation:

Given : triangle a b c where angle b is a right angle. side a b is 15 cm. side b c is 8 cm. side a c is 17 cm.

We have to select triangle from given options that are similar to ΔABC,

Two triangles are said to be  similar when their corresponding sides are in same ratios  and their corresponding angles are equal.

Consider : Right triangle J K L with right angle at K. J K is 60 centimeters. J L is 68 centimeters. K L is 32 centimeters.

FINDING CORRESPONDING RATIOS,

$\frac{AB}{JK}=\frac{15}{60}=\frac{1}{4}$

$\frac{BC}{KL}=\frac{8}{32}=\frac{1}{4}$

$\frac{AC}{JL}=\frac{17}{68}=\frac{1}{4}$

Since, ratios are equal. Thus, triangles are similar.

ΔABC ≅ ΔJKL

Consider : Right triangle D E F with right angle at E. D E is 22.5 centimeters. D F is 25.5 centimeters. E F is 12 centimeters.

FINDING CORRESPONDING RATIOS,

$\frac{AB}{DE}=\frac{15}{22.5}=\frac{2}{3}$

$\frac{BC}{EF}=\frac{8}{12}=\frac{2}{3}$

$\frac{AC}{DF}=\frac{17}{25.5}=\frac{2}{3}$

Since, ratios are equal. Thus, triangles are similar.

ΔABC ≅ ΔDEF

Thus, option (b) and (d) are correct.