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anzhelika [568]
3 years ago
9

This 2 pls i need help with explanation sum

Mathematics
1 answer:
Nataliya [291]3 years ago
4 0

9514 1404 393

Explanation:

<h3>8.</h3>

An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.

The above relation tells us ...

  ∠PRS = ∠PQR +∠QPR = 2q +2p

Then ...

  ∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p

and

  ∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior

  q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR

  p = ∠QTR = 1/2(∠QPR) . . . . . subtract q

__

<h3>9.</h3>

For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...

  ∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°

Substituting the congruent angles, this gives ...

  ∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation

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<h3>Further explanation</h3>
  • This is one of the classic problems of Euclidean geometry.
  • The angle is determined by three points, we call it A, B, C, with A ≠ C and B ≠ C.  
  • We express an angle with three points and a symbol ∠. The middle point represents constantly vertex. We can, besides, give angle names only with vertices. For example, based on the accompanying image, the angle can be symbolized as ∠BAC, or ∠CAB, or ∠A.  

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  • The obtuse angle represents an angle whose measures greater than 90° and less than 180°.  
  • The straight angle is a line that goes infinitely in both directions and measures 180°. Carefully differentiate from rays that only runs in one direction.

<u>Note:</u>

Undefined terms are the basic figure that is undefined in terms of other figures. The undefined terms (or primitive terms) in geometry are a point, line, and plane.

These key terms cannot be mathematically defined using other known words.

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  • A plane represents a planar surface that contains many points and lines. A plane extends infinitely in all four directions. It is two-dimensional. Three noncollinear points determine a plane, as there is exactly one plane that can go through these points.  
<h3>Learn more   </h3>
  1. Undefined terms are implemented to define a ray brainly.com/question/1087090
  2. Definition of the line segment brainly.com/question/909890  
  3. What are three collinear points on a line? brainly.com/question/5795008  

Keywords: the definition of an angle, the undefined term, line, point, line, plane, ray, endpoint, acute, obtuse, right, straight, Euclidean geometry

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