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Authoritative PPT Summary
"Congruent Triangles" PPT courseware
think about it
Press a triangle on the paper, draw the pattern, and cut out the cardboard according to the pattern. Are the cut cardboard and the triangle exactly the same size and shape? Can they completely overlap?
concept
Figures of the same shape and size can overlap completely when put together.
Two shapes that can completely overlap are called congruent shapes.
Two triangles that completely overlap are called congruent triangles
Representation of congruent triangles
Can you determine all the corresponding vertices, corresponding sides, and corresponding angles directly from the notation ΔABC≌ ΔDEF?
law
1. If there is a common edge, the common edge must be the corresponding edge.
2. If there are opposite vertex angles, the opposite vertex angles must be corresponding angles.
3. If there are common angles, the common angle must be the corresponding angle.
4. The sides opposite to corresponding angles are corresponding sides, and the angles opposite to corresponding sides are corresponding angles.
5. In two congruent triangles, the longest side is to the longest side, the shortest side is to the shortest side, the largest angle is to the largest angle, and the smallest angle is to the smallest angle.
Class exercises
1. Please find the corresponding sides and corresponding angles.
AB and EB, BC BD, AD EC,
∠A ∠BEC、∠D ∠C、∠ABD ∠EBC
2. If AB=3cm, BC=5cm, find the lengths of BE and BD.
Solution: ∵△ABD ≌ △EBC
∴AB=EB，BC=BD
∵AB=3cm,BC=5cm
∴BE=3cm,BD=5cm
Class summary
1. Two shapes that can overlap are called congruent shapes.
Among them: vertices that overlap each other are called corresponding vertices
The edges that overlap each other are called corresponding edges.
Angles that coincide with each other are called corresponding angles
2. Two triangles that can completely overlap are called congruent triangles.
3. "Congruent" is represented by the symbol "≌", which is pronounced as "congruent"
4. The corresponding sides and corresponding angles of congruent triangles are equal
5. When writing congruent equations, it is required to put the corresponding letters in the corresponding positions.
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"Determination of Congruent Triangles" PPT courseware 5:
"Determination of Congruent Triangles" PPT Courseware 5 Teaching Objectives In the teaching of this lesson, not only should students learn how to identify congruent triangles with sides, angles, and sides, but more importantly, students should master the method of researching problems and initially Understand the mathematical ideas of classification discussion. From...
"Determination of Congruent Triangles" PPT courseware 4:
"Determination of Congruent Triangles" PPT Courseware 4 Write the converse of the following proposition. The corresponding sides of congruent triangles are equal, the corresponding angles are equal, the corresponding sides are equal, and the corresponding angles are equal. Conjecture that each triangle has three sides and three angles , if you want to judge two triangles...
"Determination of Congruent Triangles" PPT courseware 3:
"Determination of Congruent Triangles" PPT Courseware 3 Discussion: In the above, according to the given conditions, two triangles with different shapes are drawn. This shows that when the two sides of the two triangles and the opposite angle of one of the sides are equal, , these two triangles are not necessarily congruent, do you think...