answer.
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
lawyer [7]
2 years ago
14

Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.

Mathematics
1 answer:
kolbaska11 [484]2 years ago
6 0

Answer:

See explanation

Step-by-step explanation:

Triangles ΔABC and ΔBAD are congruent. So,

  • AB ≅ BA;
  • AC ≅ BD;
  • BC ≅ AD;
  • ∠ABC ≅ ∠BAD;
  • ∠BCA ≅ ∠ADB;
  • ∠CAB ≅ ∠DBA.

Consider triangles AEC and BED. In these triangles,

  • AC ≅ BD;
  • ∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
  • ∠AEC ≅ ∠BED (as vertical angles).

So, ΔAEC ≅ ΔBED. Thus,

AE ≅ EB.

This means that segment CD bisects segment AD.

You might be interested in
Pens cost 15 pence each.
ch4aika [34]

Answer:

The amount the school pays is £32.40

Step-by-step explanation:

The cost of each pen = 15 pence

The cost of each ruler = 20 pence

The number of pens bought by the school = 150

The number of rulers bought by the school = 90

The cost reduction (discount) on the items bought = 1/5

Therefore, we have;

The total cost of the pens bought by the school = 150 × 15 = 2250 = £22.50

The total cost of the rulers bought by the school = 90 × 20 = 1800 = £18.00

The total cost of the writing materials (rulers and pens) bought by the school = £22.50 + £18.00 = £40.50

The discount = 1/5 total cost reduction = 1/5×£40.50  = $8.10

The amount the school pays = The total cost of the writing materials - The discount

The amount the school pays = £40.50 - $8.10 =  £32.40

The amount the school pays =  £32.40.

7 0
1 year ago
Is 0.15893 rational or irrational?
Ganezh [65]
It would be irrational
5 0
2 years ago
Read 2 more answers
Triangles E F G and E prime F prime G prime are shown. Angles F E G and F prime E prime G prime are 72 degrees. Angles E F G and
Karolina [17]

Answer:

We need a non-included side of one triangle

Step-by-step explanation:

By means of the AAS postulate.

The Angle-Angle-Side postulate (AAS) tells us that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

3 0
2 years ago
In circle O, central angle AOB measures StartFraction pi Over 3 EndFraction radians. Circle O is shown. Line segments A O and B
blondinia [14]

Answer:

6(pie)

Step-by-step explanation:

trust me ; )

6 0
2 years ago
Read 2 more answers
There is only one granola bar left out of a pan of 10 bars. if Will and Rachel decide to split the last granola bar what fractio
lesantik [10]
1/20. I believe. One granola bar out of ten is 1/10 and half of a granola bar (or half of 1/10) is 1/20.
6 0
1 year ago
Other questions:
  • What is the value of 3 in 630
    8·1 answer
  • The yearbook staff enlarges a picture with a length of 5 inches and a width of 7
    15·2 answers
  • The number of cubic feet of water in a curved container can be approximated by v = 0.95h2.9. use a calculator to find the amount
    5·2 answers
  • A recent poll of 85 randomly selected cable subscribers found that 39% would be willing to pay extra for a new nature channel. T
    14·2 answers
  • In triangle ABC, m a = 45 m b =65 and a = 15.05. Use the law of sines to find b. Round your answer to the nearest tenth.
    10·2 answers
  • Lines K and L are parallel,and the measure of angle ABC is 19 degrees
    11·1 answer
  • An online furniture store sells chairs for $200 each and tables for $600 each. Every day, the store can ship a maximum of 32 pie
    11·1 answer
  • A lightbulb manufacturer ships large consignments of lightbulbs to big industrial users. When the production process is function
    11·1 answer
  • There are four defenders on a soccer team. If this represents 20 percent of the players on the team, which equation can be used
    7·2 answers
  • Expand the expression: 1/3(12d + e)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!