All categories

3 years ago

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

You might be interested in

Mr.Hawkins is covering a wall with wallpaper. The rectangular wall measure 14 feet by 12 feet. each square foot of wallpaper cos

yan [13]

Answer:

$57.93

Step-by-step explanation:

14 x 12 = 168

168/2.9

6 0

2 years ago

How many triangles can you construct with the angle measures of 50, 70, and 100?

lidiya [134]

Answer:

Step-by-step explanation:

You can't construct any triangles with those angles. Because when you add all the angles of a triangle, it has to add up to 180. But when we add 50,70, and 100, it equals 220. So you can't construct any triangles.

Hope this helps.<em> (If it does, please mark me brainliest)</em>

6 0

3 years ago

A line passes through (-2, 5) and has a slope of 1/3. What is the equation Of the line in poin slope form?

vagabundo [1.1K]

Helppp12345678909876543234567

7 0

2 years ago

What are the coordinates of the centroid of a triangle with vertices D(0,1),E(2,6), and F(7,2) enter your answer in the boxes

Daniel [21]

The coordinates of centroid of given triangle are: (3,3)

Step-by-step explanation:

Given

D(0,1) = (x1,y1)

E(2,6) = (x2,y2)

F(7,2) = (x3,y3)

The centroid of a triangle when the vertices are known is given by:

$C = (\frac{x_1+x_2+x_3}{3} , \frac{y_1+y_2+y_3}{3})$

Putting the values

$C = (\frac{0+2+7}{3} , \frac{1+6+2}{3})\\C = (\frac{9}{3} , \frac{9}{3})\\= (3,3)$

Hence,

The coordinates of centroid of given triangle are: (3,3)

Keywords: Triangle, centroid

Learn more about triangles at:

#LearnwithBrainly

7 0

3 years ago

Quadrilateral A’B’C’D’ is a dilation of quadrilateral ABCD about point P. Quadrilateral ABCD is shown. Side AB is labeled 5. Sid

Stolb23 [73]

Answer: The correct option is (A) reduction.

Step-by-step explanation: Given that the quadrilateral A'B'C'D' is a dilation of the quadrilateral ABCD.

As shown in the given figure, the lengths of the sides of quadrilateral ABCD are as follows:

AB = 5 units, BC = 4 units, CD = 10 units and DA = 6 units.

And, the lengths of the sides of quadrilateral A'B'C'D' are as follows:

$A'B'=1\dfrac{1}{4}=\dfrac{5}{4}~\textup{units},~~B'C'=1~\textup{units},~~C'D'=2\dfrac{1}{2}=\dfrac{5}{2}~\textup{units},\\\\D'A'=1\dfrac{1}{2}=\dfrac{3}{2}~\textup{units}.$

We know that the dilation will be an enlargement if the scale factor is greater than 1 and it will be a reduction if the scale factor is less than 1.

Now, the scale factor is given by

$S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}\\\\\\\Rightarrow S=\dfrac{A'B'}{AB}=\dfrac{\frac{5}{4}}{5}=\dfrac{5}{4\times5}=\dfrac{1}{4}$

Since the scale factor is less than 1, so the dilation will be a reduction.

5 0

2 years ago

Read 2 more answers