Prove that the lengths of the diagonals of an isosceles trapezoid are equal

1 answer:

6 0

AD || BC
• AB = CD 
• ∠BAD = ∠CDA (a given condition ∵ ABCD is an isosceles trapezium) 

The diagonals AC and BD create two ∆'s: ∆ABD, and ∆ACD 

The two ∆'s are congruent (SAS). 

(S): AB = CD 
(A): ∠BAD = ∠CDA
(S): AD = DA (common side) 

The corresponding sides of the two ∆'s, BD and AC, are also congruent. 
(the two diagonals of the trapezium/trapezoid)

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A rectangle is 3 feet long by 4 feet wide

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Answer:

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Answer: D
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Part A:

rewona [7]

Part B - Question 1

Distance for the spacecraft to travel from Venus to Jupiter = Distance of Jupiter from Sun - Distance of Venus from Sun

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 4.838 × 10⁸ - 6.724 × 10⁷

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 483,800,000 - 67,240,000

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 416,560,000

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 4.1656 × 10⁸

Part B - Question 2

Combined distance of Mercury, Venus, and Earth from the Sun = Distance of Mercury from Sun + Distance of Venus from Sun + Distance of Earth from Sun

⇒ Combined distance of Mercury, Venus, and Earth from the Sun = 5.7909 × 10⁷ + 6.724 × 10⁷ + 9.296 × 10⁷

⇒ Combined distance of Mercury, Venus, and Earth from the Sun = 21.8109 × 10⁷

⇒ Combined distance of Mercury, Venus, and Earth from the Sun = 2.18109 × 10⁸

Distance of Neptune from the Sun = 2.793 × 10⁹

Hence, we can see that the combined distance of Mercury, Venus and Earth from the Sun is less than that of Neptune from the Sun.

Part B - Question 3

If Earth was 10 times farther away from the sun, then the new distance between the Sun and the Earth = 10 × 9.296 × 10⁷

⇒ New distance between the Sun and the Earth = 9.296 × 10⁸

Now, the Earth will be closest to Saturn, which is 8.907 × 10⁸ away from the Sun

New Distance between Earth and Saturn = Distance of Earth from Sun - Distance of Saturn from Sun

⇒ New Distance between Earth and Saturn = 9.296 × 10⁸ - 8.907 × 10⁸

⇒ New Distance between Earth and Saturn = 0.389 × 10⁸

⇒ New Distance between Earth and Saturn = 3.89 × 10⁷ (in scientific notation)

⇒ New Distance between Earth and Saturn = 38,900,000 (in standard notation)

Part B - Question 4

Speed of space shuttle = 28,000 km per hour

Time spent to travel from Saturn to Earth = $\frac{\text{Distance between Saturn and Earth}}{\text{Speed of space shuttle} }$

⇒Time spent to travel from Saturn to Earth = $\frac{\text{Distance of Saturn from Sun - Distance of Earth from Sun}}{\text{Speed of space shuttle} }$