geometry journal chapter 4 jose antonio weymann 9-3 m2 geometry/algebra

GEOMETRY JOURNAL CHAPTER 4

JOSE ANTONIO WEYMANN 9-3M2 GEOMETRY/ALGEBRA

*Equilateral *Isosceles *Scalene •Right •Acute •Obtuse •Equiangular

TRIANGLES

Triangle types:

Equilateral: Is a triangle with three congruent sides.

Isosceles: Is a triangle with at least two congruent sides.

Scalene: Is a triangle with no congruent sides

Triangle types:

Equiangular: A triangle with three congruent angles.

Acute: A triangle with three acute angles.

Right: A triangle with one right angle.

Obtuse: A triangle

Triangle Types

We use the different classifications into categories by: we combine the terms of the first slide with the ones of the second slide. We need to know the different types for next lessons and chapters. In real life we could use them for construction to know that amount of material needed in triangular shapes.

Example: Obtuse Isosceles

Parts of a triangle: Sides: are the segments that make the three sided

figure Verteces: are the points at which the sides meet

Triangle Sum Theorem: The sum of the angle measures of triangle are 180º

45º ^1= 180º

^2= 180º 90º 45º

1

2

Exterior angle: is an angle formed from one side of the triangle and the extension in the adjacent part of the side.

< 1 <2

Interior angle: is an angle formed by two sides

Parts of a triangle:

1

2 3

Exterior Angle Theorem

m<4 = m<1 + m<2 We use this theorem to find the measures

vertices we don’t know in a triangle with a exterior angle, in real life we could use this in construction to know the necessary angle for support in triangular shape bases.

Examples:

<4= 180ª m<1 +m<2= 180º

r

Examples: 55º <X m<X= 110º 55º 34º

80º <Y m<Y= 114º

Exterior Angle Theorem

Congruence in shapes & CPCT

Shapes are congruent if they have the same measure; if they are being stated as congruent the vertices have to be in the same order; they have to have same size, shape, and position.

CPCT : Corresponding Parts of Congruent Triangles

(e.g.) A B

C D AB = 4ft. 4ft.

(e.g.) # 2 E G EF congruent

to GH

F H

(e.g.) # 3

Congruence in shapes & CPCT

M

W2

SSS

SIDE-SIDE-SIDE: this postulate says if two triangles have there three sides congruent to one another, then the triangle themselves are congruent.

4cm. 4cm.

4cm. 4cm.

4cm. 4cm.

2ft. 2ft. 4ft.

2ft. 2ft. 4ft. Both triangles are congruent because of Side-

Side-Side

SSS

SIDE-ANGLE-ANGLE: this postulate says that if the sides and included angle in two triangles are congruent, then the triangles are congruent.

SAS

SAS

ANGLE-SIDE-ANGLE: this postulate says that if the two angles and the included side of two triangles are congruent, then the triangles are congruent themselves.

ASA

^1 congruent to ^2

ASA

12

ANGLE-ANGLE-SIDE: this postulate says that if two triangles have their two angles and included side are congruent, then the triangles are congruent.

AAS

AAS

The triangles are congruent because of Angle-Angle-Side

AAS

Conclusion

I hope to have covered the topics appropriately, and I believe I am ready for the exam.