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SIMILAR TRIANGLES. Pdf version with video links.
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For construction problems touch on the below images. Construction video will be played..
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𝑺𝒊𝒎𝒊𝒍𝒂𝒓 𝒄𝒊𝒓𝒄𝒍𝒆𝒔. 𝑻𝒘𝒐 𝒑𝒐𝒍𝒚𝒈𝒐𝒏𝒔 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒂𝒎𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝒔𝒊𝒎𝒊𝒍𝒂𝒓 𝒊𝒇 𝒕𝒉𝒆𝒊𝒓 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒂𝒏𝒈𝒍𝒆𝒔 𝒂𝒓𝒆 𝒆𝒒𝒖𝒂𝒍 𝒂𝒏𝒅 𝒕𝒉𝒆𝒊𝒓 𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝒊𝒏 𝒕𝒉𝒆 𝒔𝒂𝒎𝒆 𝒓𝒂𝒓𝒕𝒊𝒐 𝒐𝒓 𝒑𝒓𝒐𝒑𝒐𝒓𝒕𝒊𝒐𝒏. 𝑨𝒍𝒍 𝒓𝒆𝒈𝒖𝒍𝒂𝒓 𝒑𝒐𝒍𝒚𝒈𝒐𝒏𝒔 𝒉𝒂𝒗𝒊𝒏𝒈 𝒕𝒉𝒆 𝒔𝒂𝒎𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝒂𝒍𝒘𝒂𝒚𝒔 𝒔𝒊𝒎𝒊𝒍𝒂𝒓. 𝑺𝒊𝒎𝒊𝒍𝒂𝒓 𝒔𝒒𝒖𝒂𝒓𝒆𝒔 𝑺𝒊𝒎𝒊𝒍𝒂𝒓 𝒆𝒒𝒖𝒊𝒍𝒂𝒕𝒆𝒓𝒂𝒍 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆𝒔 𝑨𝒍𝒍 𝒄𝒊𝒓𝒄𝒍𝒆𝒔 𝒂𝒓𝒆 𝒔𝒊𝒎𝒊𝒍𝒂𝒓 𝒂𝒏𝒅 𝒕𝒉𝒆 𝒄𝒊𝒓𝒄𝒍𝒆𝒔 𝒘𝒊𝒕𝒉 𝒔𝒂𝒎𝒆 𝒓𝒂𝒅𝒊𝒖𝒔 𝒂𝒓𝒆 𝒄𝒐𝒏𝒈𝒓𝒖𝒆𝒏𝒕..
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A. B. C. D. 𝐀𝟏. 𝐁𝟏. 𝐂𝟏. 𝐃𝟏. ∠𝑨 = ∠𝑨𝟏, ∠𝑩 = ∠𝑩𝟏, ∠𝑪 = ∠𝑪𝟏, ∠𝑫 = ∠𝑫𝟏,.
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DO THIS. (i) Any two similar figures are congruent..
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Similarity of Triangles :. Two triangles are similar if Corresponding angles are equal and Corresponding sides are in the same ratio (in proportion).
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Activity. P. Q. A. B. C. 𝑨𝑷 𝑨𝑸 𝑷𝑩 𝒂𝒏𝒅 𝑸𝑪 𝑨𝑷 𝑨𝑸 𝑷𝑩 = 𝑸𝑪.
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𝑩𝒂𝒔𝒊𝒄 𝑷𝒓𝒐𝒑𝒐𝒓𝒕𝒊𝒐𝒏𝒂𝒍𝒊𝒕𝒚 𝑻𝒉𝒆𝒐𝒓𝒆𝒎 (𝑻𝒉𝒂𝒍𝒆𝒔 𝑻𝒉𝒆𝒐𝒓𝒆𝒎).
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𝑨𝒏𝒐𝒕𝒉𝒆𝒓 𝒇𝒐𝒓𝒎 𝒐𝒇 𝑩𝒂𝒔𝒊𝒄 𝑷𝒓𝒐𝒑𝒐𝒓𝒕𝒊𝒐𝒏𝒂𝒍𝒊𝒕𝒚 𝑻𝒉𝒆𝒐𝒓𝒆𝒎.
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𝑪𝒐𝒏𝒗𝒆𝒓𝒔𝒆 𝒐𝒇 𝑩𝒂𝒔𝒊𝒄 𝑷𝒓𝒐𝒑𝒐𝒓𝒕𝒊𝒐𝒏𝒂𝒍𝒊𝒕𝒚 𝑻𝒉𝒆𝒐𝒓𝒆𝒎.
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶ 1. In triangle DPQR, E and F are points on the sides PQ and PR respectively. For each of the following, state whether EF ||QR or not? PE = 3.9 cm EQ = 3 cm PF = 3.6 cm and FR = 2.4 cm PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm. PQ = 1.28 cm PR = 2.56 cm PE = 1.8 cm and PF = 3.6 cm (𝐢) 𝑮𝒊𝒗𝒆𝒏 𝑷𝑬 = 𝟑. 𝟗 𝒄𝒎, 𝑬𝑸 = 𝟑 𝒄𝒎, 𝑷𝑭 = 𝟑. 𝟔 𝒄𝒎 𝒂𝒏𝒅 𝑭𝑹 = 𝟐. 𝟒 𝒄𝒎.
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶ 1. In triangle DPQR, E and F are points on the sides PQ and PR respectively. For each of the following, state whether EF ||QR or not? PE = 3.9 cm EQ = 3 cm PF = 3.6 cm and FR = 2.4 cm PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm. PQ = 1.28 cm PR = 2.56 cm PE = 1.8 cm and PF = 3.6 cm (𝐢𝐢) 𝑮𝒊𝒗𝒆𝒏 𝑷𝑬 = 𝟒 𝒄𝒎, 𝑬𝑸 = 𝟒. 𝟓 𝒄𝒎, 𝑷𝑭 = 𝟖 𝒄𝒎 𝒂𝒏𝒅 𝑭𝑹 = 𝟗 𝒄𝒎.
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶ 1. In triangle DPQR, E and F are points on the sides PQ and PR respectively. For each of the following, state whether EF ||QR or not? PE = 3.9 cm EQ = 3 cm PF = 3.6 cm and FR = 2.4 cm PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm. PQ = 1.28 cm PR = 2.56 cm PE = 1.8 cm and PF = 3.6 cm (𝐢𝐢𝐢) 𝑮𝒊𝒗𝒆𝒏 𝑷𝑸 = 𝟏. 𝟐𝟖 𝒄𝒎, 𝑷𝑹 = 𝟐. 𝟓𝟔 𝒄𝒎, 𝑷𝑬 = 𝟏. 𝟖 𝒄𝒎 𝒂𝒏𝒅 𝑷𝑭 = 𝟑. 𝟔 𝒄𝒎.
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. In the following figures, DE ||BC..
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟏. 𝑰𝒏 ∆𝑷𝑸𝑹, 𝑺𝑻 𝒊𝒔 𝒂 𝒍𝒊𝒏𝒆 𝒔𝒖𝒄𝒉 𝒕𝒉𝒂𝒕.
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟐. 𝑰𝒏 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒇𝒊𝒈𝒖𝒓𝒆, 𝑳𝑴 ∥ 𝑪𝑩 𝒂𝒏𝒅 𝑳𝑵 ∥ 𝑪𝑫. 𝑷𝒓𝒐𝒗𝒆 𝒕𝒉𝒂𝒕.
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟑. 𝑰𝒏 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒇𝒊𝒈𝒖𝒓𝒆, 𝑫𝑬 ∥ 𝑨𝑪 𝒂𝒏𝒅 𝑫𝑭 ∥ 𝑨𝑬. 𝑷𝒓𝒐𝒗𝒆 𝒕𝒉𝒂𝒕.
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟒. 𝑷𝒓𝒐𝒗𝒆 𝒕𝒉𝒂𝒕 𝒂 𝒍𝒊𝒏𝒆 𝒅𝒓𝒂𝒘𝒏 𝒕𝒉𝒓𝒐𝒖𝒈𝒉 𝒕𝒉𝒆 𝒎𝒊𝒅 − 𝒑𝒐𝒊𝒏𝒕 𝒐𝒇 𝒐𝒏𝒆 𝒔𝒊𝒅𝒆 𝒐𝒇 𝒂 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆 𝒑𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝒕𝒐 𝒂𝒏𝒐𝒕𝒉𝒆𝒓 𝒔𝒊𝒅𝒆 𝒃𝒊𝒔𝒆𝒄𝒆𝒕𝒔 𝒕𝒉𝒆 𝒕𝒉𝒊𝒓𝒅 𝒔𝒊𝒅𝒆..
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟓. 𝑷𝒓𝒐𝒗𝒆 𝒕𝒉𝒂𝒕 𝒂 𝒍𝒊𝒏𝒆 𝒋𝒐𝒊𝒏𝒊𝒏𝒈 𝒕𝒉𝒆 𝒎𝒊𝒅 𝒑𝒐𝒊𝒏𝒕𝒔 𝒐𝒇 𝒂𝒏𝒚 𝒕𝒘𝒐 𝒔𝒊𝒅𝒆𝒔 𝒐𝒇 𝒂 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆 𝒊𝒔 𝒑𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝒕𝒐 𝒕𝒉𝒆 𝒕𝒉𝒊𝒓𝒅 𝒔𝒊𝒅𝒆..
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟔. 𝑰𝒏 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒇𝒊𝒈𝒖𝒓𝒆, 𝑫𝑬 ∥ 𝑶𝑸 𝒂𝒏𝒅 𝑫𝑭 ∥ 𝑶𝑹. 𝑺𝒉𝒐𝒘 𝒕𝒉𝒂𝒕 𝑬𝑭 ∥ 𝑸𝑹..
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟕. 𝑰𝒏 𝒕𝒉𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒇𝒊𝒈𝒖𝒓𝒆, 𝑨, 𝑩 𝒂𝒏𝒅 𝑪 𝒂𝒓𝒆 𝒑𝒐𝒊𝒏𝒕𝒔 𝒐𝒏 𝑶𝑷, 𝑶𝑸 𝒂𝒏𝒅 𝑶𝑹 𝒓𝒆𝒔𝒑𝒆𝒄𝒕𝒊𝒗𝒆𝒍𝒚 𝒔𝒖𝒄𝒉 𝒕𝒉𝒂𝒕 𝑨𝑩 ∥ 𝑷𝑸 𝒂𝒏𝒅 𝑨𝑪 ∥ 𝑷𝑹. 𝑺𝒉𝒐𝒘 𝒕𝒉𝒂𝒕 𝑩𝑪 ∥ 𝑸𝑹..
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𝐄𝐗𝐄𝐑𝐂𝐈𝐒𝐄 − 𝟖. 𝟏. 𝟖. 𝑨𝑩𝑪𝑫 𝒊𝒔 𝒂 𝒕𝒓𝒂𝒑𝒆𝒛𝒊𝒖𝒎 𝒊𝒏 𝒘𝒉𝒊𝒄𝒉 𝑨𝑩 ∥ 𝑫𝑪 𝒂𝒏𝒅 𝒊𝒕𝒔 𝒅𝒊𝒂𝒈𝒐𝒏𝒂𝒍𝒔 𝒊𝒏𝒕𝒆𝒓𝒔𝒆𝒄𝒕.
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9. Draw a line segment of length 7.2 cm and divide it in th sol p A5 ratio 5 : 3. Measure the two parts. Steps of construction : 1. Draw a Kne segment AB of length 7.2 cm. 2 Draw a ray AX wNch makhg an acute with AB. 3. Mark off 5+3 = 8 equl parts (A 1,A2 ,.... .A8) on AX with same radus 4. Join A8 and B. 5 Draw a Ene parallel to A8B at A5 AB at P. P is the recured point wtich dvides AB the ratio 5:3. 7. By meast.ring with scale we can oberve ttBt x.
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𝑨𝑨𝑨 𝑪𝑹𝑰𝑻𝑬𝑹𝑰𝑶𝑵 𝑭𝑶𝑹 𝑺𝑰𝑴𝑰𝑳𝑨𝑹𝑰𝑻𝒀 𝑶𝑭 𝑻𝑹𝑨𝑰𝑵𝑮𝑳𝑬𝑺.
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𝑨𝑨𝑨 𝑪𝑹𝑰𝑻𝑬𝑹𝑰𝑶𝑵 𝑭𝑶𝑹 𝑺𝑰𝑴𝑰𝑳𝑨𝑹𝑰𝑻𝒀 𝑶𝑭 𝑻𝑹𝑨𝑰𝑵𝑮𝑳𝑬𝑺.
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𝑺𝑺𝑺 𝑪𝑹𝑰𝑻𝑬𝑹𝑰𝑶𝑵 𝑭𝑶𝑹 𝑺𝑰𝑴𝑰𝑳𝑨𝑹𝑰𝑻𝒀 𝑶𝑭 𝑻𝑹𝑨𝑰𝑵𝑮𝑳𝑬𝑺.
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𝑺𝑨𝑺 𝑪𝑹𝑰𝑻𝑬𝑹𝑰𝑶𝑵 𝑭𝑶𝑹 𝑺𝑰𝑴𝑰𝑳𝑨𝑹𝑰𝑻𝒀 𝑶𝑭 𝑻𝑹𝑨𝑰𝑵𝑮𝑳𝑬𝑺.
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 1. Are triangles formed in each figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝐓𝐑𝐘 𝐓𝐇𝐈𝐒 ∶. 2. If pairs of the triangles are similar and then find the value of x..
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𝑨𝑨𝑨 𝑪𝑹𝑰𝑻𝑬𝑹𝑰𝑶𝑵 𝑭𝑶𝑹 𝑺𝑰𝑴𝑰𝑳𝑨𝑹𝑰𝑻𝒀 𝑶𝑭 𝑻𝑹𝑨𝑰𝑵𝑮𝑳𝑬𝑺.
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𝑳𝒆𝒕 ∆ 𝑨𝑩𝑪 ∼ ∆𝑫𝑬𝑭. A. B. C. D. E. F. 𝒕𝒉𝒆𝒏 𝒘𝒆 𝒉𝒂𝒗𝒆, 𝑨𝑩 𝑩𝑪 𝑪𝑨 𝑫𝑬 = 𝑬𝑭 = 𝑭𝑫.
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𝑬𝑿𝑬𝑹𝑪𝑰𝑺𝑬 − 𝟖. 𝟐 1. In the given figure, ∠ ADE= ∠B (i) Show that ∆ ABC ∼ ∆ ADE (ii) If AD = 3.8 cm, AE = 3.6cm, BE = 2.1 cm and BC = 4.2 cm, find DE.
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𝑬𝑿𝑬𝑹𝑪𝑰𝑺𝑬 − 𝟖. 𝟐. 2. The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle..
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𝑬𝑿𝑬𝑹𝑪𝑰𝑺𝑬 − 𝟖. 𝟐. 3. In the given figure, AB || CD || EF. given that AB=7.5 cm, DC= y cm EF = 4.5 cm and.
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𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒘𝒂𝒍𝒌𝒆𝒅 𝒃𝒚 𝒈𝒊𝒓𝒍 𝒇𝒓𝒐𝒎 𝒕𝒉𝒆 𝒇𝒐𝒐𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒍𝒂𝒎𝒑 𝒑𝒐𝒔𝒕 𝒊𝒏 𝟒 𝒔𝒆𝒄𝒐𝒏𝒅𝒔 𝒊𝒔 𝑩𝑫 = 𝟒 × 𝟏. 𝟐 = 𝟒. 𝟖 𝒎 𝑳𝒆𝒕 𝒕𝒉𝒆 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝒈𝒊𝒓𝒍 𝒃𝒆 𝑫𝑬 = ′𝒙′ 𝒎 𝑰𝒏 ∆𝑨𝑩𝑬 𝒂𝒏𝒅 ∆𝑪𝑫𝑬, ∠𝑬 = ∠𝑬 (∵ 𝒄𝒐𝒎𝒎𝒐𝒏 𝒂𝒏𝒈𝒍𝒆).
Scene 50 (20m 38s)
𝑬𝑿𝑬𝑹𝑪𝑰𝑺𝑬 − 𝟖. 𝟐 5. 𝐆𝐢𝐯𝐞𝐧 𝐭𝐡𝐚𝐭 ∆𝑨𝑩𝑪 ∼ ∆𝑷𝑸𝑹. 𝐂𝐌 𝐚𝐧𝐝 𝐑𝐍 𝐚𝐫𝐞 𝐫𝐞𝐬𝐩𝐞𝐜𝐭𝐢𝐯𝐞𝐥𝐲 𝐭𝐡𝐞 𝐦𝐞𝐝𝐢𝐚𝐧𝐬 𝐨𝐟 ∆𝑨𝑩𝑪 𝐚𝐧𝐝.