"Constructing Triangles with Rulers and Compasses" Triangle PPT Teaching Courseware

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"Constructing Triangles with Rulers and Compasses" Triangle PPT Teaching Courseware

Part One: Learning Objectives

1. Under the conditions of two angles, the angle between two sides and three sides respectively, be able to use a ruler and compass to construct a triangle.

2. Be able to communicate the rationality of the drawing process and results with peers based on the conditions of congruence of triangles.

Use ruler and compass to make triangles PPT, part 2 content: activity exploration

Exploration point 1: Make a known triangle (two angles and one side)

The basic elements of a triangle are _____ and ______.

1. Given the two angles of a triangle and the included side, find the triangle.

Known: ∠α, ∠β, line segment c.

Find: △ABC, let ∠A=∠α, ∠B=∠β, AB=c.

For sides and angles, you want to do ____ first, then ___, and finally _____.

practice:

(1) As ∠DAF=∠α;

(2) Intercept line segment AB=c on ray AF;

(3) Taking B as the vertex and BA as one side, let ∠ABE=∠β, and BE intersects AD at point C.

△ABC is the triangle you want to construct.

Compare the triangle you made with the triangle made by your partner. Are they congruent? Why?

Exploration point 2: Make a known triangle (two sides and one corner)

1. Given the two sides and included angles of a triangle, find the triangle.

Known: line segments a, c, ∠α.

Find: △ABC, let BC=a, AB=c, ∠ABC=∠α.

Method: (1) Draw a line segment BC=a

(2) With B as the vertex and BC as the side, draw the angle ∠DBC=∠α

(3) Intercept line segment BA=c on ray BD

(4) Connect AC

△ABC is the triangle you want to construct.

Compare the triangle you made with the triangle made by your partner. Are they congruent? Why?

Use ruler and compass to make triangles PPT, part three: analysis of examples

For example, given the three sides of a triangle, find the triangle.

Known: line segments a, b, c.

Find: △ABC, so that AB=c, AC=b, BC=a.

Try to analyze and make this triangle yourself and write down how to do it.

Use a ruler and compass to make a triangle PPT, Part 4: Inspection in class

1. Using basic drawing, the only triangle that cannot be drawn is ( )

A. Three known sides B. Two sides and their angle are known

C. Two angles and their included sides are known D. Two sides and the opposite angle of one of them are known

2. Known: right angle, line segments a, b

Find the solution: right triangle ABC, let BC=a, AC=b

3. Given ∠α and ∠β and line segment a, use a ruler and compass to construct a triangle so that one interior angle is equal to ∠α, the other interior angle is equal to ∠β, and the opposite side of ∠α is equal to a.

Use ruler and compass to make triangles PPT, Part 5: Class summary

What did you learn in this lesson?

1. Learned to use a ruler and compass to make triangles

2. Further verified the conditions of congruent triangles.

Use a ruler and compass to make a triangle PPT, Part 6: Personalized homework

1. The right triangle that cannot be constructed using a ruler or compass is ( )

A. Given the hypotenuse and a right-angled side

B. Two right angled sides are known

C. Two acute angles are known

D. An acute angle and a right angled side are known

2. Given the line segments a, b and ∠α, find △ABC so that it has one interior angle equal to ∠α, and the opposite side of ∠α is equal to a, and the other side is equal to b.

3． As shown in the figure, given ∠AOB, follow the steps below to draw the graph:

(1) Take point O as the center of the circle, draw an arc with an appropriate length as the radius, intersect OA at D, and intersect OB at point E;

(2) Draw arcs with D and E as the center points and a length greater than 1/2DE as the radius. The two arcs intersect at point C inside ∠AOB;

(3) Draw ray OC;

Based on the above drawing steps, try to explain why ray OC bisects ∠AOB?

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For more information about the "Triangle Constructing Triangles with Ruler and Compasses" PPT courseware, please click on the Triangle PPT Constructing Triangles with Ruler and Compasses PPT tag.

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"Constructing Triangles with Ruler and Compass" Triangle PPT:

"Constructing Triangles with a Ruler and Compass" Triangle PPT Part One Content: Learning Objectives 1. Be able to use a ruler and compass to make a triangle under the condition that two angles and their included sides, two sides and their included angles, and three sides are given respectively. 2. Understand how to make a triangle. The rationality of the diagram method. ... ... ... Use a ruler..

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Update Time: 2024-11-18

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