"Interior and exterior angles of a triangle" PPT

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"Interior and exterior angles of a triangle" PPT

Part One: Review the past and learn the new

1. Related concepts of triangles:

1. What is a triangle:

A figure composed of three line segments that are not on the same straight line and connected end to end is called a triangle.

2. Vertex: Use a capital letter to represent such as A, B, C

3. Side: side AB, side BC, side AC

4. Angle (interior angle): ∠A, ∠B, ∠C

5. The triangle is recorded as: △ABC

6. Opposite angle: The angle opposite to side BC is ∠A

Opposite side: The opposite side of ∠C is BA

Interior angles and exterior angles of triangles PPT, part 2 content: classroom exercises

It is known that the two sides of the triangle are 12cm and 15cm respectively. Find the value range of the third side.

15-12

That is: 3cm

How to determine the range of values ​​for the third side of a triangle:

The difference between the two sides

Quick check

There are two wooden sticks with lengths of 5cm and 8cm respectively. Now take another wooden stick and form a triangle with them. How long do you think the third one should be?

Is it okay to use a wooden stick with a length of 3cm? Why?

What about a wooden stick with a length of 14cm?

Given the lengths of both sides of the triangle, the length range of the third side is:

It is greater than the difference between these two sides and less than the sum of these two sides.

Interior angles and exterior angles of triangles PPT, Part 3: Classification of triangles

by angle

right triangle

oblique triangle

Acute triangle

obtuse triangle

Divide by sides

Scalene triangle (irregular triangle)

isosceles triangle

An isosceles triangle with only two equal sides

Equilateral triangle

Interior angles and exterior angles of a triangle PPT, Part 4 content: Sum of interior angles and exterior angles of a triangle

What is the relationship between an exterior angle of a triangle and the three interior angles of a triangle?

∠ ACD+ ∠ ACB=180°

∠ACD= ∠ A+ ∠ B

∠ACD> ∠A

∠ACD> ∠ B

Exterior angle + adjacent interior angle = 180˚

An exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles.

The exterior angle of a triangle is greater than any interior angle that is not adjacent to it.

The sum of the exterior angles of a triangle

For each interior angle of a triangle, take one of the two adjacent exterior angles. The sum of the three exterior angles thus obtained is called the sum of the exterior angles of the triangle.

Thinking: The sum of the interior angles of a triangle is equal to 180°, then what is the sum of the exterior angles of the triangle?

Interior angles and exterior angles of a triangle PPT, part 5: analysis of examples

Example 1 As shown in the figure, D is a point on the side BC of △ABC, ∠B=∠BAD, ∠ADC=80˚, ∠BAC=70˚. Find:

(1) The degree of ∠ B; (2) The degree of ∠ C.

Solution: (1)∵ ∠ADC is the exterior angle of �ABD (known)

∴∠ADC=∠B+∠BAD=80˚

(An exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles)

And ∵ ∠B=∠BAD

∴∠B=40˚

(2) ∵ in �ABC ∠ B+ ∠ BAC+ ∠ C= 180 ˚

∴∠ C= 180 ˚ - ∠ B - ∠ BAC

= 180˚-40˚-70˚

=70˚

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"Interior and Exterior Angle of a Triangle" PPT download:

"Interior Angle and Exterior Angle of a Triangle" PPT download part one: Think about the sum of the three interior angles of a triangle. How can you verify it? Tips: Try putting the three angles together to try the verification method: such as Figure: Extend BC to CD, and make CE∥AB then...

"Interior and Exterior Angle of Triangle" PPT courseware:

"Interior Angle and Exterior Angle of a Triangle" PPT courseware Part One Content: Interior Angle and Exterior Angle of a Triangle Review Questions: 1. What are the interior angles of a triangle? 2. What is the relationship between the three interior angles of a triangle? Jigsaw Puzzle: Tear off the three interior angles of a triangle..

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Update Time: 2024-07-26

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