The corresponding points in two graphs are called symmetrical points about this straight line, and this straight line is called the axis of symmetry. So two figures are symmetrical about a straight line, which is also called that the two figures form an axial symmetry.
Isosceles triangle is a special kind of triangle, which has other special properties besides "isosceles".
(1) Its two base angles coincide; ② The crease in the middle is perpendicular to the bottom edge; ③ The crease bisects the apex angle; (4) the crease divides the bottom edge in two.
The two base angles of an isosceles triangle are equal (abbreviated as "equilateral corners")
Inference 1. The bisector of the vertex of an isosceles triangle bisects the bottom and is perpendicular to the bottom.
Inference 2. All angles of an equilateral triangle are equal, and each angle is equal to 60.
Now the nature theorem and inference of isosceles triangle are expressed in symbolic language as follows:
①∫ab = AC (known) ∴∠ B =∠ C (equilateral and isometric)
② ∵ AB = AC, and equally divided with AD ∠BAC (known).
∴ BD = CD, AD⊥BC (three in one)
③∫AB = AC, and AD is the midline (known).
∴∠ bad =∠ CAD, AD⊥BC (three in one)
④∫ab = AC, AD⊥BC (known)
∴∠ bad =∠ CAD, BD = CD (three in one)
⑤∫AB = BC = AC (known)
∴∠a =∠b =∠c = 60 (all angles of an equilateral triangle are equal, and each angle is equal to 60).
, using the properties of isosceles triangle:
Example 3, (1) If one angle in an isosceles triangle has a degree of 50, the degrees of the other two angles are.
(2) If the degree of one angle in an isosceles triangle is 100, the degrees of the other two angles are.
(3) The sum of the outer angles of the two bottom angles and the top angle of an isosceles triangle is equal to 260, so the top angle of this triangle is 0 and the bottom angle is 0.
(4) If the ratio of the top angle to the bottom angle of an isosceles triangle is 1:4, the degrees of the three angles are respectively.
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