# Angles formed by the intersection of two straight lines

Educational minimum in geometry 3rd quarter.7th grade.

Triangles. Theoretical part.

1. Triangles are:

Signs of equality of triangles Sign I (on two sides and the angle between them) If two sides and the angle between them of one triangle are respectively equal to two sides and the angle between them of another triangle, then such triangles are equal. II sign (on the side and two adjacent angles) If the side and two angles adjacent to it of one triangle are respectively equal to the side and two angles adjacent to it of another triangle, then such triangles are congruent. III sign (on three sides) If three sides of one triangle are respectively equal to three sides of another triangle, then such triangles are equal.

3. Height, median, bisector of a triangle. The altitude is the perpendicular from the vertex of the triangle to the line containing the opposite side. The median is the line segment that connects the vertex of a triangle with the midpoint of the opposite side. The bisector of a triangle is a segment of the bisector of an angle that connects a vertex to a point on the opposite side.

4. Properties of an isosceles triangle

1) The angles at the base of an isosceles triangle are equal

2) The bisector drawn to the base of the isosceles

triangle is the median and height

Practical part

 1. Using a ruler and a protractor, construct the medians, bisectors, and heights of these triangles. 2. One side of the triangle is 24 cm, the second is 18 cm more than the first, and the third side is 2 times less than the second. Find the perimeter of the triangle. 3. The side of an isosceles triangle is 16cm, and the base is 20cm. Find the perimeter of this triangle. 4. The perimeter of an isosceles triangle is 28 cm, and the side is 10 cm. Find the base of the triangle. 5. In the figure, AC = CD, BC = CE. Prove that ΔABC = ΔEDC. 6. Given: BD = CD. Prove that AB = AC. 7. In the figure ∠1 = ∠2,∠3 = ∠4, AB = 8cm. BC = 6cm. Find sides AD and CD of triangle ACD. 8. In the figure MK = KE, OE = 6cm, ∠MKE = 48°, ∠POE = 90°. Find the side of ME and ∠CCO. 9. The line intersects the sides of the angle A at points B and C so that AB = AC. Prove that ∠1=∠2.  ten. The bisectors AM and CK of the angles at the base AC of an isosceles triangle ABC intersect at point O. Prove that ΔAOC is isosceles. 11. In the figure AC = AD, BC = BD. Find the angle BAC if ∠BAD = 25°. 12.  In the figure, AB = CD, AC = BD. Prove that ΔBOC is isosceles.

Parallel lines. Theoretical part.

1 Lines are called parallel if they lie in the same plane and do not intersect.

2 Axiom of parallelism: Through a point not lying on a given line, there is only one line parallel to the given

Angles formed by the intersection of two straight lines