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TRANSCRIPT
Ray
Line
Intersecting Lines
Parallel Lines
Line Segment
RAY: A part of a line, with one endpoint, that continues without end in one direction
LINE: A straight path extending in both directions with no endpoints
LINE SEGMENT: A part of a line that includes two points, called endpoints, and all the points between them
INTERSECTING LINE: The two lines in the same plane are not parallel, they will intersect at a common point. Those lines are intersecting lines. Here C is the common point of AE and DB
PARALLEL LINES: Lines that never cross and are always the same distance apart
Perpendicular Lines
Two lines that intersect to form a right angles
Right Angle:An angle that forms a square corner
Acute Angle:An angle less than a right angle
Obtuse Angle:An angle greater than a right angle
Straight Angle: It is equal to 180°
Reflex Angle: An angle which is more than 180° but less than 360°
Complementary Angles: Two angles adding up to 90° are called complementary angles.
Here ABD + DBC are Complementary.
Supplementary Angles: Two angles adding up to 180° are called supplementary.
ABD + DBC are supplementary
Transversal: A Transversal is a line that intersect two parallel lines at different points.
Vertical Angles: Two angles that are opposite angles
1 2
3 4
5 6
7 8
t∠1 ≅ ∠ 4∠2 ≅ ∠ 3∠5 ≅ ∠ 8∠6 ≅ ∠ 7
Linear Pair: Two angles that form a l ine (sum=180°)
1 2
3 4
5 6
7 8
t
∠5+∠6=180∠6+∠8=180∠8+∠7=180∠7+∠5=180
∠1+∠2=180∠2+∠4=180∠4+∠3=180∠3+∠1=180
Corresponding Angles: Two angles that occupy corresponding positions are equal.
∠1 ≅ ∠ 5∠2 ≅ ∠ 6∠3 ≅ ∠ 7∠4 ≅ ∠ 8
t
1 2
3 4
5 6
7 8
Alternate Interior Angles: Two angles that lie between parallel lines on opposite side.
∠3 ≅ ∠ 6∠4 ≅ ∠ 5
1 2
3 4
5 6
7 8
Co-Interior Angles: Two angles that lie between parallel lines on the same side of the transversal
1 2
3 4
5 6
7 8
3 +∠5 = 1804 +∠6 = 180
Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal
1 2
3 4
5 6
7 8
2 ≅ ∠ 71 ≅ ∠ 8
Angle Sum Property Of Triangle: The sum of the angles of a triangle is 180°.
1
23
1 + 2 + 3 = 180°
Property of Exterior Angle: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Angle 1,2,3 are exterior angles of triangle
• Vertically Opposite Angles are equal
To Proof – Vertically Opposite Angles are equal
Solution - ∠b + ∠n = 180° ( LINEAR PAIR)
∠b + ∠m = 180° ( LINEAR PAIR)
EQUATING BOTH THE EQUATIONS
→ ∠b + ∠n = ∠b + ∠m
→ ∠n = ∠m
Hence Proved
• Angle Sum Property Of A Triangle is 180°
To Proof -Angle Sum Property Of a Triangle is 180°
Construction - Draw ↔m parallel to BC
Solution - ∠4 = ∠1 (Alternate Interior Angles)
∠5 = ∠2 (Alternate Interior Angles)
∠3 + ∠4 + ∠5 = 180° ( Angles on the same line are supplementary)
Substituting the values
∠3 + ∠1 + ∠2 = 180° (Angle Sum Property)
Hence Proved
Made by:
Shaik Mallika