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Authoritative PPT Summary
"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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