Geometry Journal 4 Michelle Habie 9 3 Triangles

Geometry Journal 4 Michelle Habie 9 -3

Triangles: Sides: Scalene (3 sides are different) Equilateral (3 sides are thesame) Issoceles (2 sides are equaland 1 isdifferent) Angles: Acute (3 anglesmeasurelessthan 90°) Right (1 anglemeasures 90°) Obtuse(1 anglesmeasuresgreaterthan 90°) We use each type of triangle according to its sides and its angle measurement because each of them, has different properties and uses.

Examples: Issoceles. Triangle Right Triangle to measure the shape of the building. Obtuse– roofof a house. Equilateral- to build games made of iron. Scalene

Partsof a Triangle: 1 angle Parts: 3 sides 3 interior angles 1 exterior angle for each side Hypotenuse Hyoptenuse 1 side 1 angle The exterior angle is formed by the extension of one side of the triangle. The exterior angle has two remote interior angles which are non-adjacent to the exterior one. An interior angle is formed when two sides of a triangle meet. Triangle Sum Theorem: It states that the sum of the 3 interior angles of any triangle have to be equal to 180 degrees.

Ang. A+ Ang. B+ a. NG. C =180 X+19+2 x+1+100=180 3 x+120=180 3 x=60 X=20 Examples: Interior: 3 x+5 B A 118 2 x+3 3 x+5+2 x+13=118 5 x+18=118 5 x=100 X=20 5 x+1 99 X+19 X+8 A B 100 2 x+1 5 x++x+8=99 6 x+9=99 6 x=90 x=15 Exterior: 3 x-10 2 z+1 2 25 X+15 10 6 z-9 4 1 3 C

Exterior Angle. Theorem: States that the exterior angle is the same as the sum of the two remote interior angles. How can it be used? It can be used in navigation to find angles by knowing two and find the target or the place they are leading to.

Congruence: Congruenceforshapesmeansthattheobjectshavethes ameshapeandthesamemeasurementswhilecorresp onding in shapesmeanssidesthatocupythesameposition. Whileprovingtwotriangles are congruentyou may needgoprovethecorrespondingsidesorangles are congruentandthenjumpinto a conclusionthatthetwotriangles are congurent by the CPCTC. Meaningthatthe. Congruent. Partsofthe. Congruent. Trian gles are alwayscongruent.

CPCT Examples: 4 cm 10 cm 8 cm 8 cm 8 cm 4 cm 8 cm 13 cm 10 cm 6 cm 13 cm 15 cm 13 cm 6 cm 13 cm

SSS Postulate: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

Examples: 16 cm 9 cm 9 cm 5 cm 16 cm 24 cm 16 cm

SAS Postulate: This type of postulate is used to prove that two triangles are congruent. This postulate says that if two sides of one triangle and the included angle of it, and congruent=not to the corresponding two sides and the included angle of the second triangles, than the two figures are congruent.

Examples: 1. V C E D A Y F X B ABC congruent 1 EFD 4 2 6 3 U 5 123 congruent 456 Z XYZ congruent W UVW

ASA Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the traingles are congruent.

Examples: 25 25 32 32 25 100 25 76 100 90 90 76 30 27 15 30 15 27

AAS Theorem: If twoangles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent.

Examples: = angle 30 30 75 75 8 in 21 14 9 cm 21 14 8 in