Question

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Similarity Flow Chart Proofs Part 5

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Answer 1

• See below

Explanation:

#10

According to diagram we have

• TU ║ WV and TV is transversal
• ∠T ≅ ∠V as alternate interior angles
• TX ≅ VX
• ∠TXU ≅ ∠WXV as vertical angles

Conclusion

• ΔTXU ≅ ΔWXV by ASA (angle-side-angle)

#11

ABC and DCB are right triangles but corresponding sides have different ratio

• 5/5 ≠ 13/12

So triangles are not similar

#12

According to Pythagorean the missing hypotenuse is

• 
  `√(3^2+4^2)=√(25) =5`

The triangles have three congruent pairs of sides (3, 4 and 5 units) so are congruent by SSS (or HL)