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Authoritative PPT Summary
"Vertical" PPT courseware 3
Independent learning + group communication
Read textbook P19-P21 and think about the following questions
1. What is the definition and representation of vertical?
2. How to draw a vertical line?
3. What are the properties of vertical lines?
4. What is the distance from a point to a straight line?
What is the definition and representation of vertical?
One of the straight lines is called the perpendicular to the other straight line, and their intersection is called the vertical foot.
Among the four angles formed by the intersection of two straight lines, if one of the angles is a right angle, the two straight lines are said to be perpendicular to each other.
For example: As shown in the figure, straight line AB and straight line CD intersect at point O, OE⊥AB.
Given that ∠BOD=45°, find the degree of ∠COE.
Solution: ∵OE⊥AB (known)
∴∠AOE=90° (vertical definition)
∵∠AOC=∠BOD=45° (the opposite vertex angles are equal)
∴∠COE = ∠AOC+ ∠AOE
=45°+90°
= 135°
Given a straight line l passing through a point B outside the straight line and a point A on the straight line respectively, how many ways do you have to draw the perpendicular line of l?
Method 1: Use a triangle ruler
Method 2: Use a protractor
Steps: One lean, two pass, three draw
Drawing a perpendicular to a known line segment or ray is actually a perpendicular to the straight line where the known line segment or ray is located through a known point.
Let's find fault together
Among the following statements, the correct one is ( )
A. Through a point outside the straight line and a certain point on the straight line, countless straight lines can be drawn perpendicular to this straight line.
B. The perpendicular line of the straight line can be drawn through a point on the straight line and a certain point outside the straight line.
C. A perpendicular line of this ray can be drawn through a point outside the ray.
D. If two straight lines do not intersect, then the two straight lines may be perpendicular to each other.
practise
1.The distance from a point to a straight line is ( )
A. The perpendicular segment from a point outside the straight line to the straight line
B. The length of the perpendicular segment from a point outside the straight line to the straight line
C. The length of the perpendicular line from a point outside the straight line to the straight line
D. The distance from a point outside the straight line to any point on the line
2. As shown in the figure, AD⊥BD, BC⊥CD, AB=a cm, BC=b cm, then the value range of BD is ( )
A. Less than a cm
B. Greater than b cm
C. Less than a cm or larger than b cm
D. Less than a cm and greater than b cm
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