What must be true for lines a and b to be parallel lines? Select four options.
2 answers:
The question is missing figure and the options. So, the figure is attached alongwith the options
Answer:
Correct options: (1), (2) , (7) and (8)
Step-by-step explanation:
Given:
Lines a and b are parallel.
Consider a║b and 'd' be a transversal then,
Statements Reasons
1. ∠BXZ = ∠AZP = 58° Corresponding angles are equal
∴ m∠2 = 58°
2. ∠BYC = ∠XYZ = ° Vertically opposite angles are equal
Now, consider a║b and 'c' be a transversal then,
Statements Reasons
1. ∠XYZ = ∠QZU = ° Corresponding angles are equal
∴ m∠1 = °
2.∠PZA + ∠PZQ + ∠QZU = 180° Sum of angles on a straight line is 180°.
3. Substitution property
4. Combining like terms
5. Subtraction property of equality
∴
6. Division property of equality
Plug in , we get
= 56°
= 66°
So,
Hence, options (1), (2) , (7) and (8) are correct.
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Answer:
Area of Triangle = 1/2 bh
A = 1/2 (16 cm x 10 cm)
A = 160 cm2/2
A = 80 square cm
Area of Circle = d2/4
A = 3.14 x (16 cm)2 / 4
A = 3.14 x 256 cm2 / 4
A = 803.84 cm2 / 4
A = 200.96 cm2
Area of Half Circle = 200.96 cm2 / 2
A = 100.48
Composite Figure = Area of Triangle + Area of half Circle
Area of Composite Figure = 80 cm2 + 100.48 cm2
Area of Composite Figure = 180.48 cm2