Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to...
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Transcript of Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to...
![Page 1: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/1.jpg)
Properties of a Triangle
mABC + mBCA + mCAB = 1800
(Internal angles of any triangle add up to 1800)
mPAB + mQBA + mACR = 3600
(Exterior angles of any triangle add up to 3600)
A
B C
P
RQ
![Page 2: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/2.jpg)
Properties of a Triangle (Contd)
A triangle which has all three of its sides equal in length is calledan equilateral triangle.
All angles of an equilateraltriangle are congruent and measure 600 each.
a a
a
600
600 600
A triangle which has two of its sides equal in length is called an isosceles triangle.
The base angles of an isosceles triangle are always equal.
Ø0 Ø0
![Page 3: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/3.jpg)
Incenter of a Triangle
The point where the three angle bisectors of a triangle meet.
![Page 4: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/4.jpg)
Circumcenter of a Triangle
The point where the three perpendicular bisectors of a triangle meet.
![Page 5: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/5.jpg)
Centroid of a Triangle
The point where the three medians of the triangle intersect. The 'center of gravity' of the triangle
![Page 6: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/6.jpg)
Orthocenter of a Triangle
The point where the three altitudes of a triangle intersect.
![Page 7: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/7.jpg)
Properties of Equilateral Triangle
With an equilateral triangle, the radius of the incircle is exactly half the radius of the circumcircle.
a
![Page 8: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/8.jpg)
Congruence of Triangles - SSS Test
Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.
![Page 9: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/9.jpg)
Congruence of Triangles - SAS Test
Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.
![Page 10: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/10.jpg)
Congruence of Triangles - ASA Test
Triangles are congruent if any two angles and their included side are equal in both triangles.
![Page 11: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/11.jpg)
Congruence of Triangles - AAS Test
Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
![Page 12: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/12.jpg)
Congruence of Triangles - HL Test
Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
![Page 13: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/13.jpg)
Pythagoras Theorem
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In ABC if mABC = 900 then,l(AC)2 = l(AB)2 + l(BC)2
A
B C
![Page 14: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/14.jpg)
30°- 60°- 90° Triangle
In a 30°- 60°- 90° Triangle, the hypotenuse is double the side opposite to 30° angle and the side opposite to 60° angle is Sqrt(3) times the side opposite to 30° angle.
A
B C
2 Units
1 Unit
Units3
600
300900
![Page 15: Properties of a Triangle m ABC + m BCA + m CAB = 180 0 (Internal angles of any triangle add up to 180 0 ) m PAB + m QBA + m ACR = 360 0 (Exterior.](https://reader030.fdocuments.us/reader030/viewer/2022013101/5697bf741a28abf838c7fd04/html5/thumbnails/15.jpg)
45°- 45°- 90° Triangle
In a 45°- 45°- 90° Triangle, sides opposite to 450 angles are of equal length, and, Hypotenuse is sqrt(2) times either side.
A
B C
Units1 Unit
1 Unit
2
450
450900