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Authoritative PPT Summary
"Triangle" PPT courseware 3
teaching objectives
1. Experience hands-on operations, exploration and discovery, and verification of conjectures, discover, reveal and initially apply the relationship between the three sides of a triangle, that is, the activity process of "the sum of any two sides of a triangle is greater than the third side", develop spatial concepts, cultivate preliminary logical thinking abilities, and practice Operation ability, experience the fun of "doing mathematics" and "using mathematics".
2. Experience the process of exploring, discovering, and applying the relationship between the three sides of a triangle, enhance the spirit of courage to explore, appreciate the practical value of mathematics, feel the rigor of mathematics and the joy of successful exploration of mathematics, enhance the awareness of mathematics application and the spirit of communication and cooperation, and improve students' mathematical literacy.
Experimental exploration
1. Group experiment:
Each group prepares four wooden or cardboard strips, with lengths of 4cm, 6cm, 7cm, and 11cm respectively. Try to pick any three of them and connect them end to end to form a triangle. Is it successful? Keep good experimental records.
2. Exchange findings:
Question 1: Can any three line segments form a triangle? Tell us which experiment failed and why?
Question 2: What can you discover from the experiment?
Discuss
(1) On the night of the Lantern Festival, lanterns were lit on the roof beams. Which one is longer, the wire with blue lanterns or the wire with red lanterns? Explain your reasons.
Use the patterns you discovered to fill in the blanks
AB+AC_______BC
AB+BC_______AC
AC+BC_______AB
(2) In a triangle, what is the relationship between the sum of any two sides and the length of the third side?
Why? What conclusions can you draw from this?
practise
1. It is known that the length of one side of an isosceles triangle is 3 and the length of one side is 6, then its perimeter is ( ).
2. The lengths of the four line segments are 5cm, 6cm, 8cm, and 13cm respectively. () triangles can be formed with any three of them as sides.
4. Taking the following three line segments of each set of lengths as sides, what triangle can be formed ()
A. 5cm, 3cm, 9cm B. 5cm, 3cm, 7cm
C.5cm, 3cm, 8cm D.6cm, 4cm, 2cm
4. The length of one side of an isosceles triangle is 4 and the length of one side is 9. Its perimeter is ()
A.17B.22C.17 or 22D.13
6.Answer
It is known that the perimeter of an isosceles triangle is 14cm and the ratio of the base to one waist is 3:2. Find the length of each side.
Compliance testing
A multiple choice question
1. Taking each set of line segments of the following lengths as sides, what is an isosceles triangle that can be formed ().
A.1,2,1 B.2,2,1
C.1, 3, 1 D.2, 2, 5
2. One side of an isosceles triangle is equal to 5cm and the other side is equal to 10cm. Then the third side should be equal to ()
A.5cm B.10cm C.5 or 10cm D.12cm
Two answer questions
1. Xiaoying wants to make a triangular wooden frame. There are two wooden sticks with lengths of 8 cm and 5 cm. If the length of the third wooden stick is required to be an integer, how many options can be chosen for the length of the third wooden stick?
2. It is known that the perimeter of an isosceles triangle is 20
If the waist length is 7, what is the base length?
If the base length is 7, what is the waist length?
If the length of one side is 7, what are the lengths of the other two sides?
Expansion and extension
The lengths of two sides of a triangle are 3 and 9 respectively, and the perimeter is an even number. Find the length of the third side of the triangle.
Harvest and experience
1. Learned the relationship between the three sides of a triangle
2. Be able to determine whether three line segments form a triangle.
3. Knowing the lengths of both sides of the triangle, the value range of the third side can be determined.
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