Download presentation

1
**Triangle Fundamentals**

Intro to G.10 Triangle Fundamentals Modified by Lisa Palen

2
**Triangle What’s a polygon?**

Definition: A triangle is a three-sided polygon. What’s a polygon?

3
Polygons Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. These figures are not polygons These figures are polygons

4
**Definition of a Polygon**

A polygon is a closed figure in a plane formed by a finite number of segments that intersect only at their endpoints.

5
**Triangles can be classified by:**

Their sides Scalene Isosceles Equilateral Their angles Acute Right Obtuse Equiangular

6
**Classifying Triangles by Sides**

Scalene: A triangle in which no sides are congruent. BC = 5.16 cm B C A BC = 3.55 cm A B C AB = 3.47 cm AC = 3.47 cm AB = 3.02 cm AC = 3.15 cm Isosceles: A triangle in which at least 2 sides are congruent. HI = 3.70 cm G H I Equilateral: A triangle in which all 3 sides are congruent. GI = 3.70 cm GH = 3.70 cm

7
**Classifying Triangles by Angles**

Obtuse: 108 44 28 B C A A triangle in which one angle is.... obtuse. Right: A triangle in which one angle is... right.

8
**Classifying Triangles by Angles**

Acute: 57 47 76 G H I A triangle in which all three angles are.... acute. Equiangular: A triangle in which all three angles are... congruent.

9
**Classification of Triangles Flow Charts Venn Diagrams**

with Flow Charts and Venn Diagrams

10
**Classification by Sides**

polygons Polygon triangles Triangle scalene isosceles Scalene Isosceles equilateral Equilateral

11
**Classification by Angles**

polygons Polygon triangles Triangle right acute equiangular Right Obtuse Acute obtuse Equiangular

12
**Naming Triangles We name a triangle using its vertices.**

For example, we can call this triangle: ∆ABC ∆ACB Review: What is ABC? ∆BAC ∆BCA ∆CAB ∆CBA

13
**Parts of Triangles Every triangle has three sides and three angles.**

For example, ∆ABC has Sides: Angles: CAB ABC ACB

14
**Opposite Sides and Angles**

Side opposite of BAC : Side opposite of ABC : Side opposite of ACB : Opposite Angles: Angle opposite of : BAC Angle opposite of : ABC Angle opposite of : ACB

15
**Interior Angle of a Triangle**

An interior angle of a triangle (or any polygon) is an angle inside the triangle (or polygon), formed by two adjacent sides. For example, ∆ABC has interior angles: ABC, BAC, BCA

16
Exterior Angle An exterior angle of a triangle (or any polygon) is an angle that forms a linear pair with an interior angle. They are the angles outside the polygon formed by extending a side of the triangle (or polygon) into a ray. Exterior Angle Interior Angles A For example, ∆ABC has exterior angle ACD, because ACD forms a linear pair with ACB. D B C

17
**Interior and Exterior Angles**

The remote interior angles of a triangle (or any polygon) are the two interior angles that are “far away from” a given exterior angle. They are the angles that do not form a linear pair with a given exterior angle. For example, ∆ABC has exterior angle: ACD and remote interior angles A and B Exterior Angle Remote Interior Angles A D B C

18
Triangle Theorems

19
**m<A + m<B + m<C = 180**

Triangle Sum Theorem The sum of the measures of the interior angles in a triangle is 180˚. m<A + m<B + m<C = 180 IGO GeoGebra Applet

20
Third Angle Corollary If two angles in one triangle are congruent to two angles in another triangle, then the third angles are congruent.

21
**Third Angle Corollary Proof**

Given: The diagram Prove: C F statements reasons 1. A D, B E 2. mA = mD, mB = mE 3. mA + mB + m C = 180º mD + mE + m F = 180º 4. m C = 180º – m A – mB m F = 180º – m D – mE 5. m C = 180º – m D – mE 6. mC = mF 7. C F 1. Given 2. Definition: congruence 3. Triangle Sum Theorem Subtraction Property of Equality Property: Substitution Definition: congruence QED

22
**Corollary Each angle in an equiangular triangle measures 60˚. 60 60**

23
Corollary There can be at most one right or obtuse angle in a triangle. Example Triangles???

24
Corollary Acute angles in a right triangle are complementary. Example

25
**Exterior Angle Theorem**

The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Remote Interior Angles A Exterior Angle D Example: Find the mA. B C 3x - 22 = x + 80 3x – x = 2x = 102 x = 51 mA = x = 51°

26
**Exterior Angle Theorem**

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. GeoGebra Applet (Theorem 1)

27
**Special Segments of Triangles**

28
**Introduction There are four segments associated with triangles:**

Medians Altitudes Perpendicular Bisectors Angle Bisectors

29
**Median - Special Segment of Triangle**

Definition: A segment from the vertex of the triangle to the midpoint of the opposite side. B A D E C F Since there are three vertices, there are three medians. In the figure C, E and F are the midpoints of the sides of the triangle.

30
**Altitude - Special Segment of Triangle**

The perpendicular segment from a vertex of the triangle to the segment that contains the opposite side. Definition: B A D F In a right triangle, two of the altitudes are the legs of the triangle. B A D F I K In an obtuse triangle, two of the altitudes are outside of the triangle.

31
**Perpendicular Bisector – Special Segment of a triangle**

A line (or ray or segment) that is perpendicular to a segment at its midpoint. Definition: The perpendicular bisector does not have to start from a vertex! R O Q P Example: M L N C D A E A B B In the isosceles ∆POQ, is the perpendicular bisector. In the scalene ∆CDE, is the perpendicular bisector. In the right ∆MLN, is the perpendicular bisector.

Similar presentations

OK

Blue – 2/23/2015 Gold – 2/24/2015. 1. Name 2 pair of alternate interior angles 5 & 3 and 4 & 1 2. What is the sum of m 1 + m 2 + m 3? 180°

Blue – 2/23/2015 Gold – 2/24/2015. 1. Name 2 pair of alternate interior angles 5 & 3 and 4 & 1 2. What is the sum of m 1 + m 2 + m 3? 180°

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

By appt only movie post Ppt on american vs british accent Ppt on class 10 hindi chapters books Ppt on non ferrous minerals and rocks Ppt on culture of kerala Ppt on railway track cross Ppt on save environment photos Ppt on sbi net banking Ppt on db2 introduction to logic Ppt on density based traffic light control