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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

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A 3 foot tall globe standing next to a woman cast an 8 ft shadow. if the woman cats a shadow that is 16ft long , then how tall i
My name is Ann [436]

The woman is 6 foot tall

<h3>What is proportion?</h3>

Proportion can be defined as the mathematical comparison of two numbers.

These numbers could be numbers, elements, set or people

From the information given, we have that;

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if the globe is 3 foot tall and casts a shadow of 8ft

Then the woman is x foot tall to cast a shadow of 16ft

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8x = 24

Make 'x' the subject

x = 48/ 8

x = 6 foot

Thus, the woman is 6 foot tall

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brainly.com/question/1781657

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2 years ago
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castortr0y [4]

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3 years ago
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Answer please<br>.........​
Anna007 [38]

Hey there!

The perimeter of the floor plan is 30 inches.

Perimeter is length + length + width + width, so we can do 9 + 9 + 6 + 6 = 30

The area of the floor plan is 54 inches²

Area is length x width, so we can do 9 x 6 = 54

The perimeter of the actual size is 105 feet

First, we can solve the dimensions for the actual size. We know that 2 inches = 7 feet, so we can do 7/2 and get 3.5. This means that for every 1 inch, it's 3.5 feet. Then, we multiply the dimensions by 3.5:

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Then we solve for perimeter. Perimeter is length + length + width + width, so we can do 31.5 + 31.5 + 21 + 21 = 105

The area of the actual size is 661.5 inches²

Area is length x width, so we can do 31.5 x 21 = 661.5

Hope this helps! Tell me if you need more help.

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3 years ago
What is the value of largest integers x such that 112/2^x is an integer.​
Gennadij [26K]

Answer:

x = 4

Step-by-step explanation:

16 × 7 = 112

2^4 = 16

so that is the answer

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