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"Perpendicular Bisectors of Line Segments" PPT courseware
teaching objectives
1. Be able to tell the theorem and converse theorem of the perpendicular bisector of a line segment, and be able to use these two theorems differently.
2. Understand the application of mathematics learning methods, observation, generalization, verification, comparison, etc. in this lesson.
3. Understand that mathematics comes from life and serves real life, and experience the application value of mathematics.
Do it yourself (folding method): Draw the vertical bisector MN of the line segment AB, with the vertical foot as C; pick any point P on MN to connect PA and PB; measure: the lengths of PA and PB, what can you find?
PA=PB P1A=P1B
What rules can you draw from this?
Proposition: The distance between a point on the perpendicular bisector of a line segment and the two endpoints of the line segment is equal.
Application examples:
example 1. As shown in the figure, in ΔABC, the perpendicular bisector MN of side BC intersects AB at point M and BC at point N respectively. The perimeter of ΔBMC is 23, and BM=7. Find the length of BC.
Solution: ∵ MN is the perpendicular bisector of line segment BC BM=7
∴CM=BM=7
∵Perimeter of ΔBMC=23
∴BM+CM+BC=23
∴BC=23-CM-BM=23-7-7=9
Example 2. As shown in the figure, BC=BA, MN bisects BC perpendicularly. If the perimeter of △ABC is 28 and CA=8, find the perimeter of: △DCA.
Solution: ∵ △ABC has a perimeter of 28, CA=8
BC=BA
∴2BA+CA=28
∴BA=10
∵ MN bisects BC perpendicularly
∴BD=DC
∴ △Perimeter of △DCA=DC+DA+CA=BD+DA+CA=BA+CA=10+8=18
After class discussion:
1. As shown in the figure, in ΔABC, DE is the perpendicular bisector of AC. The perimeters of ΔABC and ΔABD are 18 cm and 12 cm respectively. Find the length of line segment AE.
2. As shown in the figure, in ΔABC, ∠BAC = 120°, ∠C= 30°, DE is the perpendicular bisector of line segment AC, find the degree of ∠BAD.
Class summary:
The properties of the perpendicular bisector of a line segment and its application are the focus of this lesson. By applying its properties, we can prove that two line segments are equal, and we can also solve for the length of the line segment.
The straight line MN is perpendicular to the line segment AB and bisects the line segment AB. We call the straight line MN the perpendicular bisector of the line segment AB.
A line segment is an axially symmetrical figure, with one axis of symmetry being the perpendicular bisector of the line segment.
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"Perpendicular bisectors of line segments" PPT courseware 8:
"Perpendicular Bisectors of Line Segments" PPT Courseware 8 Teaching Objectives 1. Be able to tell the theorem and converse theorem of perpendicular bisectors of line segments, and be able to use these two theorems differently. 2. Understand the application of mathematics learning methods, observation, generalization, verification, comparison, etc. in this lesson. 3..