In each of the following figures, you find who triangles. Indicate whether the triangles are similar. Give reasons in support of your answer.
Answers
Answer:
Triangles (i),(ii),(iii) are similar.
Step-by-step explanation:
(i)
2.3 / 4.6 = 4/8 = 5/10
½ = ½ = ½
Corresponding sides of two similar triangles are proportional
Therefore, by SSS criterion of similarity these two triangles are similar.
Hence, we can say that these two triangles are similar.
(ii) PQ || BC
In ΔAPQ and ΔABC
∠APQ =∠B [corresponding angles]
∠PAQ =∠BAC [common]
ΔAPQ∼ΔABC
[By AA Similarity criterion]
Therefore, by AA criterion of similarity these two triangles are similar.
Hence, we can say that ΔAPQ∼ΔABC are similar.
(iii)
Corresponding sides of two similar triangles are proportional
In ΔABC and ΔDEC
AC/DC = BC/EC = 5/3
∠ ACB = ∠DCE [vertically opposite angles]
ΔABC ~ΔDEC
[By SAS Similarity criterion]
Therefore, by SAS criterion of similarity these two triangles are similar.
Hence, we can say that ΔABC ~ΔDEC are similar.
(iv)
Corresponding sides of two similar triangles are proportional
24/12 ≠ 25/13 ≠ 7/5
Here, in these two triangles the sides are not in proportional.
Hence, the triangles are not similar.
(v)
Corresponding sides of two similar triangles are proportional
3 ½ / 1 ⅙ = 2 ⅓ / 1 ¾
7/2 / 7/6 = 7/3 / 7/4
7/2 × 6/7 = 7/3 × 4/7
3/1 ≠ 4/3
Here, in these two triangles the sides are not in proportional.
Hence, the triangles are not similar.
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Answer:
Triangles (i),(ii),(iii) are similar.
Step-by-step explanation:
(i)
2.3 / 4.6 = 4/8 = 5/10
½ = ½ = ½
Corresponding sides of two similar triangles are proportional
Therefore, by SSS criterion of similarity these two triangles are similar.
Hence, we can say that these two triangles are similar.
(ii) PQ || BC
In ΔAPQ and ΔABC
∠APQ =∠B [corresponding angles]
∠PAQ =∠BAC [common]
ΔAPQ∼ΔABC
[By AA Similarity criterion]
Therefore, by AA criterion of similarity these two triangles are similar.
Hence, we can say that ΔAPQ∼ΔABC are similar.
(iii)
Corresponding sides of two similar triangles are proportional
In ΔABC and ΔDEC
AC/DC = BC/EC = 5/3
∠ ACB = ∠DCE [vertically opposite angles]
ΔABC ~ΔDEC
[By SAS Similarity criterion]
Therefore, by SAS criterion of similarity these two triangles are similar.
Hence, we can say that ΔABC ~ΔDEC are similar.
(iv)
Corresponding sides of two similar triangles are proportional
24/12 ≠ 25/13 ≠ 7/5
Here, in these two triangles the sides are not in proportional.
Hence, the triangles are not similar.
(v)
Corresponding sides of two similar triangles are proportional
3 ½ / 1 ⅙ = 2 ⅓ / 1 ¾
7/2 / 7/6 = 7/3 / 7/4
7/2 × 6/7 = 7/3 × 4/7
3/1 ≠ 4/3
Here, in these two triangles the sides are not in proportional.
Hence, the triangles are not similar.