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
taurus [48]
3 years ago
11

Complete the missing parts of the paragraph proof. Draw a perpendicular from P to AB. Label the intersection C. We are given tha

t PA = PB, so PA ≅ PB by the definition of . We know that angles PCA and PCB are right angles by the definition of . PC ≅ PC by the . So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by . Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of perpendicular bisector.
Mathematics
2 answers:
zvonat [6]3 years ago
6 0
<span>1) We are given that PA = PB, so PA ≅ PB by the definition of the radius.

</span>When you draw a perpendicular to a segment AB, you take the compass, point it at A and draw an arc of size AB, then you do the same pointing the compass on B. Point P will be one of the intersections of those two arcs. Therefore PA and PB correspond to the radii of the arcs, which were taken both equal to AB, therefore they are congruent. 
 
2) We know that angles PCA and PCB are right angles by the definition of perpendicular.

Perpendicularity is the relation between two lines that meet at a right angle. Since we know that PC is perpendicular to AB by construction, ∠PCA and ∠PCB are right angles.
 
3) PC ≅ PC by the reflexive property congruence.

The reflexive property congruence states that any shape is congruent to itself.

4) So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by CPCTC (corresponding parts of congruent triangles are congruent). 

CPCTC states that if two triangles are congruent, then all of the corresponding sides and angles are congruent. Since ΔACP ≡ ΔBCP, then the corresponding sides AC and BC are congruent.
 
5) Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of the perpendicular bisector. 

<span>The perpendicular bisector of a segment is a line that cuts the segment into two equal parts (bisector) and that forms with the segment a right angle (perpendicular). Any point on the perpendicular bisector has the same distance from the segment's extremities. PC has exactly the characteristics of a perpendicular bisector of AB. </span>
Readme [11.4K]3 years ago
6 0

1) congruent segments

2)perpendicular lines

3)reflexive proterty

4)CPCTC

You might be interested in
2 Points
Mashcka [7]

Answer:

C

Step-by-step explanation:

Factor: -7x^2 -5x+18

Factor -1 out of 7x^2 -5x +18:

−(7x^2+5x−18)

Factor.

1. 18 is negative, so a negative number multiplied by a postive number.

2. You can't factor 7, so 7x times x.

(7x−9)(x+2)

4 0
3 years ago
When asked to write a point slope equation for a line passing through the points (-4,-7) and (3,2) a student wrote y-2=-9/7(x-3)
AleksAgata [21]
First let's find the slope
Slope formula: 
\frac{y_2-y_1}{x_2-x_1} =slope
Given the two coordinates: 
(-4,-7) (3,2) 
 x1,y1  x2,y2

Plug these numbers into the formula
\frac{2-(-7)}{3-(-4)} = \frac{9}{7}
In this case the mistake that was made was that the student wrote the slope negative instead of positive
Final answer: 
<span>y-2=9/7(x-3)</span>
8 0
2 years ago
Is Figure B a scale copy of Figure A?
Lana71 [14]
Yes
Reason - figure b has been increased by 3 (x3 for each side)
Eg. figure b - 1. Figure a - 3
7 0
1 year ago
Read 2 more answers
Write decimal system equivalent of the binary number 1101<br>​
mel-nik [20]

Answer:

answer should be 13

Step-by-step explanation:

look to photo

4 0
3 years ago
Read 2 more answers
Numbers 10, 100, 1,000, and so on are called
wlad13 [49]
I do believe that those are called numbers
8 0
3 years ago
Read 2 more answers
Other questions:
  • Lenz father is paying for a $20 meal. He has a 15%-off coupon on his meal. After the discount, a 7% sales tax is applied. How mu
    6·1 answer
  • Given that when x is reduced by 17% the answer is y, express x in terms of y.
    15·1 answer
  • Write the equation of a circle with a diameter having the endpoint so of (0,4) and (6,-4). Thanks
    14·1 answer
  • Whats the correct answer??
    13·1 answer
  • From your conclusions in part E, how many triangles can be constructed based on the given conditions?
    10·2 answers
  • One number is five more than three times a second number. The sum of the numbers is 37. What are the numbers?
    8·2 answers
  • What is the slope of the line?
    13·2 answers
  • Please help!!!!!!!!!!
    13·1 answer
  • 3. (1,-6) (-5,8)<br> What is the answer
    13·1 answer
  • Which equation represents a linear function rule for the following set of ordered pairs?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!