"Right Triangle" PPT Courseware 2

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"Right Triangle" PPT Courseware 2

review:

(1) What is a right triangle?

A triangle with one right angle is called a right triangle

Generally expressed by "Rt△",

For example, the right triangle ABC is expressed as "Rt△ABC"

(2) A right triangle is a special type of triangle. In addition to the properties of a triangle, what other properties does it have?

Question 1: In Rt△ABC, ∠C=900, what is the quantitative relationship between ∠A and ∠B? Why?

In Rt△ABC, ∠C=900,

∴∠A +∠B=900

Theorem 1: The two acute angles of a right triangle are complementary to each other.

1. Consolidation exercises:

(1) In a right triangle, one acute angle is 520, then the other acute angle is _____;

(2) In Rt△ABC, ∠C=900, ∠A -∠B =300, then the degrees of ∠A and ∠B are _____ respectively;

(3) As shown in the figure, in Rt△ABC, ∠ACB=900, CD is the height on the hypotenuse AB, then,

The angle that is complementary to ∠B is ___________,

The angle that is complementary to ∠A is ___________,

The angle equal to ∠B has ___________,

The angle equal to ∠A has___________.

In △ABC, if ∠A + ∠B =900, is it a right triangle?

According to the sum of the interior angles of a triangle, ∠A + ∠B + ∠C =1800. Because ∠A + ∠B =900, so ∠C =900, so △ABC is a right triangle.

1. Determination theorem: A triangle with two complementary angles is a right triangle.

Theorem 2: In a right triangle, the midline of the hypotenuse is equal to half of the hypotenuse.

Proposition: The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse

In Rt△ABC, ∠ACB=900,

∵CD is the midline on the hypotenuse AB

∴CD=1/2AB

(CD=AD=BD)

summary

Properties of right triangles

1. The two acute angles of a right triangle are complementary to each other.

2. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.

3. In a right triangle, the side opposite to angle 300 is equal to half of the hypotenuse.

Determination of right triangle

A triangle with two complementary angles is a right triangle.

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Update Time: 2024-09-30

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