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2 years ago

Given: AD = BC and BCD = ADC Prove: DE = CE

Mathematics

2 answers:

Romashka-Z-Leto [24]2 years ago

7 0

Answer:

1. AD ≅ BC [Given]

2. ∠ADC ≅ ∠BCD [Given]

3. DC ≅ DC [reflexive property]

4. ΔADC ≅ ΔBCD [SAS]

5. ∠DAE ≅ ∠CBE [CPCTC]

6. ∠DEA ≅ ∠CEB [def. of vertical angles]

7. ∠DEA ≅ ∠CEB [vertical angles theorem]

8. ΔAED ≅ ΔBEC [AAS]

9. DE ≅ CE [CPCTC]

Step-by-step explanation:

Just finished mine :D

erastova [34]2 years ago

3 0

Answer:

According to AD=BC So AC=BD

Step-by-step explanation:

AD = BC and angle ADC = angle BCD

we have to prove AC = BD

let's see ∆ADC and ∆BCD

AD = BC [ given ]

angle ADC = angle BCD [ given ]

CD = CD

from S - A - S

∆ADC congruence ∆BCD

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A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10m greater than the other side.

DanielleElmas [232]

Answer:

The length of the fence needed to surround this garden is 188 meters.

Step-by-step explanation:

Given : A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10 m greater than the other side.

To find : The length of the fence needed to surround this garden if the area of the vegetable garden is 2184 m² ?

Solution :

Let the one side of rectangle be 'x'.

Then the other side is 'x+10'.

The area of the rectangle is 2184 m²,

i.e. $x(x+10)=2184$

$x^2+10x-2184=0$

Solve by middle term split,

$x^2+52x-42x-2184=0$

$x(x+52)-42(x+52)=0$

$(x+52)(x-42)=0$

$x=-52,42$

Reject negative value,

The side of the rectangle is 42 m.

The other side is 42+10=52 m

The perimeter of the rectangle is $P=2(l+b)$

$P=2(42+52)$

$P=2(94)$

$P=188$

Therefore, the length of the fence needed to surround this garden is 188 meter.

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2 years ago

Kiesha’s quality-control manager told her she must have 97% of her clocks functioning properly. She found a report that said 6 o

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Answer:

Step-by-step explanation:

Kiesha will have more than 97% of the products working.

Kiesha’s experimental probability is 1/50

When the inventory is 4000 clocks, the prediction is that 3920 clocks will work.

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2 years ago

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Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

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Answer:

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Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

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$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

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chubhunter [2.5K]

Answer:

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Step-by-step explanation:

You must evaluate the function f first. Division by 0 is undefined.

Therefore, The composition cannot be evaluated.

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2 years ago

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