Want to create interactive content? It’s easy in Genially!

Get started free

WEEK 26-EXPLORING-ANGLE-RELATIONSHIPS-IN-TRIANGLES

VIMSCHOOL

Created on September 30, 2024

Start designing with a free template

Discover more than 1500 professional designs like these:

Transcript

Exploring Angle Relationships in Triangles

Objectives

Start

Story

Interior Angles and Triangles

Exterior Angles

Geometric Problems

Summary

Story

Interior Angles and Triangles

The angles inside the triangle are called interior angles. For example, in triangle ABC:

Example 1:

🗨️

α, β and γ are the interior angles of △ABC

Proposition: The sum of the interior angles of a triangle is always 180 degrees.

Example 2:

In △ABC:

α + β + γ = 180° That is: 60°+60°+60° = 180°

Exterior Angles

An exterior angle is formed outside the triangle by one side and the extension of another side.

🗨️

Example 3:

In △ABC:

δ and ε are exterior angles.

In total, there are six exterior angles.

Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Example 2:

In △ABC:

δ = α + γ That is: 120° = 60°+60°

Demonstration:

β and δ are supplementary

β + δ =180°

α + β + γ =180°

β =180° - α - γ

180° - α - γ + δ =180°

δ = α + γ

Geometric Problems

Click here to draw >

Roof Inclination

If the angle at the peak of the roof is 90°, what's the inclination angle of the roof?

In order to protect from raining and snow, the roof of your house must have certain inclination (red)

90° + 2β = 180º 2β = 180° - 90° 2β = 90° β = 45°

β = 45º

Solution

1/2

Find the missing angle

2/2

Find the two missing angles.

Summary

TRIANGLE GEOMETRY

INTERIOR ANGLES

EXTERIOR ANGLES

ANGLES IN A TRIANGLE

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

8TH-EXPLORING-ANGLE-RELATIONSHIPS-IN-TRIANGLES-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MATERIAL

It is highly advised to have:

  • Grid paper.
  • Pencils of different colors.
  • Eraser.
  • A rule.
  • A compass.
  • A Protactor.
  • A calculator.
  • Geogebra installed on your phone/tablet/computer (or use online version).
un título genial aquí

El contenido visual es un lenguaje transversal, universal, como la música. Somos capaces de entender imágenes de hace millones de años, incluso de otras culturas. No nos gusta aburrir. No queremos ser repetitivos. Comunicar como siempre aburre y no engancha. Lo hacemos diferente. Hacemos sabotaje al aburrimiento. Creamos lo que al cerebro le gusta consumir porque le estimula.

Enlace

"MA.8.GR.1 Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles." MA.8.GR.1.5 Solve problems involving the relationships of interior and exterior angles of a triangle. MA.8.AR.2.1 Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides. MA.K12.MTR.1.1 Actively participate in effortful learning both individually and collectively.

un título genial aquí

El contenido visual es un lenguaje transversal, universal, como la música. Somos capaces de entender imágenes de hace millones de años, incluso de otras culturas. No nos gusta aburrir. No queremos ser repetitivos. Comunicar como siempre aburre y no engancha. Lo hacemos diferente. Hacemos sabotaje al aburrimiento. Creamos lo que al cerebro le gusta consumir porque le estimula.

Enlace

un título genial aquí

El contenido visual es un lenguaje transversal, universal, como la música. Somos capaces de entender imágenes de hace millones de años, incluso de otras culturas. No nos gusta aburrir. No queremos ser repetitivos. Comunicar como siempre aburre y no engancha. Lo hacemos diferente. Hacemos sabotaje al aburrimiento. Creamos lo que al cerebro le gusta consumir porque le estimula.

Enlace