Directions: Given two sides of a triangle, find a range of possible lengths for the third side. 7. 4 cm, 17 cm

8. 24 ft, 52 ft

9. 9 yd, 32 yd

10.16 km, 17 km

11. If a triangle has lengths of 27 m and 11 m,
39ft
17ft
35ft
22ft
16ft

12. If a triangle has lengths of 3 ft and 54 ft,
check all the possible lengths for the third check all the possible lengths for the third
side.
51 ft
53 ft
55 ft
57 ft
58 ft

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Step-by-step explanation:

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step-by-step explanation:

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answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.