1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
algol [13]
3 years ago
9

Suppose that ABCD is a trapezoid, with AB parallel to CD, and diagonals AC and BD intersecting at P. Explain why (a) triangles A

BC and ABD have the same area; (b) triangles BCP and DAP have the same area; (c) triangles ABP and CDP are similar; (d) triangles BCP and DAP need not be similar.

Mathematics
1 answer:
lora16 [44]3 years ago
8 0

Answer:

A trapezoid ABCD is show below,

AB || CD

AC and BD are diagonals intersecting at P.

(a)

In Δ ABC and ABD,

Area of triangle ABC = Area of triangle ABD

Because,

Area of triangle ABC = 1/2 × Base × Height

Base = AB

Height = h, which is same for both the triangle that's why,

Area of triangle ABC = Area of triangle ABD

(b)

As we know that,

Area of triangle ABC = Area of triangle ABD

On subtracting the area of triangle ABP from both the triangles, we get

Area of triangle ABC - area of triangle ABP = Area of triangle ABD - area of triangle ABP

⇒ area of triangle BCP = area of triangle DAP

Hence, triangles BCP and DAP have the same area.

(c)

In triangle ABP and CDP,

∠ABP = ∠CDP (opposite interior angles are equal between two parallel lines)

∠APB = ∠CPD (opposite angles are equal)

∠BAP = ∠DCP (opposite interior angles are equal between two parallel lines)

Therefore,

By AAA similarity

Triangles ABP and CDP are similar.

(d)

In triangle BCP and DAP,

Only ∠BCP = ∠APD (opposite angles are equal).

Therefore,

Triangles BCP and DAP need not be similar.

You might be interested in
The population of a town grows exponentially. After 1 year, the population is 34,560. After 2 years, the population is 37,325. W
Vladimir [108]
Exponential growth has the form:

F=Ir^t, F=final amount, I=initial amount, r=rate, t=time.

First let's solve for the rate, r, using the points provided...

37325/34560=(Ir^2)/(Ir^1)

r≈1.08  

Now find the initial amount...

34560=I(1.08)^1

I=32000 so now we have the entire equation, using x and y...

y=32000(1.08)^x

6 0
2 years ago
Read 2 more answers
What is the dimensions of a box 8 cubic feet
Nesterboy [21]

You can't tell.  The volume doesn't tell you the dimensions.  It only tells you
what the product of the three dimensions is, but not what anyone of them is.
There are an infinite number of different possibilities.

Example:  Volume = 8 cubic feet

The dimensions of the box could be

Length = 2-ft,  Width = 2-ft,  Height = 2-ft
or
1 x 1 x 8
or
1 x 2 x 4
or
1 x 3 x 2-2/3
or
1 x 5 x 1.6
or
1 x 6 x 1-1/3
or
1 x 7 x 1-1/7
or
2 x 3 x 1-1/3
or
2 x 5 x 0.8
or
2 x 6 x 2/3
or
2 x 7 x 4/7
or
2 x 8 x 1/2
.
.
etc.


8 0
3 years ago
What is the value for ƒ(x) = 3 squard 2x+1 when x=1/2
MrRa [10]
The answer is 10 as you simply plug in x in the f(x) problem so 3*2(.5)+1=10
6 0
3 years ago
What are all of the x-intercepts of the continuous function in the table? (0, 8) (–4, 0) (–4, 0), (4, 0) (–4, 0), (0, 8), (4, an
crimeas [40]

Answer:

The  x-intercepts of the continuous function in the table are:

(-4,0) and (4,0).

Step-by-step explanation:

We are given a table of values of the continuous functions as:

(0, 8) (–4, 0) (–4, 0), (4, 0)

The x-intercept of a function is a point on the x-axis i.e. where y=0. (i.e. The x-intercept is where a line crosses the x-axis ).

Here y=f(x).

Hence from the given set of values we have:

f(x)=0 when x= -4 and x=4.

Since we are given the points as (-4,0) and (4,0).

Hence, the x-intercepts of the function f(x) is: (-4,0) and (4,0).


5 0
2 years ago
What is the mode?<br> What is the median?<br> What is the range?
Marina CMI [18]

<h2>ANSWER : </h2>

<h2><<< In this case, the mode is 9 seconds. The median is the middle number in a list of numbers ordered from smallest to largest. so 10 is the median of this set of results. The range is the difference between the lowest value and the highest value, so the range here is 15 - 9 = 6. </h2>

8 0
2 years ago
Other questions:
  • The height (h) of a fireball launched from a Roman candle with an initial velocity of 64 feet per second is given by the equatio
    5·1 answer
  • A music festival sold two types of tickets, day passes and weekend passes. The day passes were $57, and the weekend pass was $97
    11·1 answer
  • What is 1.265 rounded to the nearest tenth
    7·2 answers
  • Segment MN has endpoints at M(-5, 4) and N(7, -5). What is the midpoint of MN???? PLZ HELP
    6·1 answer
  • What is the equation of this line in slope-intercept form? y=−3x−1y=−3x−1 y=−13x−1y=−13x−1 y=3x−1y=3x−1 y = 3x + 1
    15·1 answer
  • three tanks are capable of holding 108 168l and 180 litre of milk determine the capacity of the greatest resource which can be u
    14·1 answer
  • precalculus help! i'm having some trouble with my summer assignment. help would be very appreciated :)))
    15·2 answers
  • 0.034 is 1/10 of 0.0034
    9·1 answer
  • Can you help me please?
    6·2 answers
  • Pre-algebra
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!