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statuscvo [17]
3 years ago
13

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

Mathematics
2 answers:
Romashka-Z-Leto [24]3 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]3 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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Greeley [361]
First account: $6500
Second account: $8500

Set x is amount of money in first account
=> x + 2000 is money in second account.
X*3% + (x+2000)*4% = 535
=> x = (53500 - 8000) / 7
X = 45500 / 7 = 6500
=> account #1 = x = 6500
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8 0
3 years ago
In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.
Elena L [17]

Given:

PQRS is a circle, PQT and SRT  are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT  are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

m\angle SPQ+m\angle QRS=180^\circ

81^\circ+m\angle QRS=180^\circ

m\angle QRS=180^\circ-81^\circ

m\angle QRS=99^\circ

Now, SRT  is a straight line.

m\angle QRT+m\angle QRS=180^\circ             (Linear pair)

m\angle QRT+99^\circ=180^\circ

m\angle QRT=180^\circ-99^\circ

m\angle QRT=81^\circ               ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

m\angle PQR=m\angle QRT+m\angle QTR

x=81^\circ+22^\circ

x=103^\circ

Therefore, the value of x is 103 degrees.

4 0
3 years ago
If the circumference of a circle measures 12π cm, what is the area of the circle in terms of π?
frez [133]
So the formula for the circumference of a circle is π x diameter
Since we know the the circumference already, we just divide that by π:

12π / π = 12

Now we halve the diameter to get the radius:
12 / 2 = 6 

The area of a circle is π x radius²
So the area is:

·π x 6² = 36π·  (or 113 not in terms of π) 
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sergiy2304 [10]

Answer:

yes to 5

Step-by-step explanation:

divide 45 by 9 and u get 5

3 0
2 years ago
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Answer:

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