ЭШ · Суралцах · 180 бодлого
Geometry Геометр ба хэмжигдэхүүн
Plane geometry through solids: triangles and their centers, similarity, right-triangle trig, quadrilaterals, circles, areas, coordinate methods, and 3D measurement. Exam geometry chains two or three facts per problem — the order here builds those chains.
Сургалтын хөтөлбөр (БСШУСЯ, А/492): 10.7, 10.8, 10.12, 11.5
01 · Курс
12 нэгжээс 12 нь бэлэн — хичээл, дадлага, өөрийгөө шалгах тесттэй. Хичээлүүд одоогоор англи хэлээр; монгол орчуулга дараа нэмэгдэнэ.
01 Triangles & Congruence Classify triangles and prove the 180° angle sum; the exterior-angle theorem and triangle inequality; and the congruence shortcuts SSS, SAS, ASA, AAS, HL with CPCTC and isosceles triangles. Start 02 Relationships in Triangles Perpendicular bisectors and the circumcenter, angle bisectors and the incenter, medians and the centroid, altitudes and the orthocenter, the midsegment theorem, and inequalities inside one triangle. Start 03 Similarity Ratio, proportion and scale factor; similar polygons; the AA·SSS·SAS similarity shortcuts; the side-splitter theorem; perimeter and area ratios; and dilations with indirect measurement. Start 04 Right Triangles & Trigonometry The Pythagorean theorem and its converse; classifying triangles; special right triangles; the SOH-CAH-TOA trig ratios; finding sides; and angles of elevation and depression with inverse trig. Start 05 Quadrilaterals & Polygons Interior and exterior angle sums for any polygon; parallelograms and how to prove them; rectangles, rhombi, squares, trapezoids, and kites; and the quadrilateral family tree. Start 06 Circles Parts of a circle and central angles; arcs and chords; inscribed angles; tangents; the chord/secant/tangent angle relationships; and arc length and sector area. Start 07 Area & Perimeter Areas of parallelograms, triangles, trapezoids, rhombi and kites; regular polygons via the apothem; circles and sectors; and composite and shaded figures. Start 08 Coordinate Geometry Distance, midpoint, and slope; equations of lines and circles; proofs with coordinates — the course capstone. Start 09 Surface Area & Volume Prisms, cylinders, pyramids, cones, and spheres — wrapping and filling 3-D solids, then combining them into composite figures. Start 10 Lines & Planes in Space The rules of 3D: how planes are determined, how lines can miss each other without being parallel, and how to measure distances and angles when things leave the flat page. Start 11 Cylinders & Cones The round solids you can unroll: the cylinder's secret rectangle, the cone's secret pie-slice, the 3-4-5 triangle hiding in every ice-cream cone, and the truncated cone in your coffee cup. Start 12 Spheres The perfect solid: every slice is a circle, the surface is exactly four shadow-circles, the volume is two-thirds of its can — and Archimedes liked that last fact enough to put it on his tombstone. Start