
Learn to identify similar triangles using the similarity postulate and theorems, including the triangle proportionality theorem and the midsegment theorem. Apply these to relate corresponding sides, areas, and geometric means.
Explores solving problems with similar triangles, using exterior angle theorem and pythagorean theorem to find x, y, z, and ratios in multiple triangle cases.
Master solving with similar triangles and pythagorean theorem to find perimeters and missing sides, then apply tangent and circle theorems, and resolve log m minus log n.
Use two pairs of similar triangles formed by parallel lines to derive the third side as ab/(a+b) and solve related problems through proportional reasoning.
The triangle proportional segment theorem states that a line parallel to a triangle side divides the other sides proportionally. The side splitter theorem uses similar triangles to find segment values.
Three parallel lines cut two transversals, forcing proportional divisions (a/b = c/d) and enabling problem solving with triangle proportional segment reasoning.
Apply the midsegment theorem: a segment through midpoints is parallel to third side and half its length. Use similar triangles to derive area relations and solve right-triangle and Heron-based problems.
Derive and apply the ratio of areas for similar triangles: area ratios equal the squares of corresponding side ratios, with worked examples using equilateral and isosceles configurations.
Learn to compute area ratios of similar triangles by using the square of corresponding side lengths, express areas as big minus smaller, and apply height calculations from Pythagorean theorem.
Explore how the ratio of areas in similar triangles relates to squared side ratios, and apply isosceles triangle height, a perpendicular bisector, and Pythagorean reasoning to find area.
Explore geometric mean of triangles using similar right triangles, derive three formulas, solve for sides c, d, h, and apply them to find triangle area from base and height.
Explore geometric mean in triangles through coordinate diagrams, calculate area and perimeter, and apply Thales theorem and inscribed angles to diverse examples.
In this comprehensive course, students will delve into the fascinating world of similar triangles, exploring their properties, applications, and real-world connections.
The course focuses on definition of similar triangles, Similarity Postulate and Theorems, Triangle Proportional Segment Theorem, Parallel Proportional Segment Theorem, Mid-Segment Theorem, Ratio of areas of similar triangle and Geometric mean of triangles. Each of the objectives has well structured examples to illustrate what will be taught.
In addition to the main objectives, the course helps the students to develop critical thinking and problem-solving skills through the interactive lessons and activities. The learner needs to be conversant with ratio, proportion and the knowledge of basic triangle theorems like Pythagorean Theorems, Exterior Angle Theorems, angle on a straight line before he/she enrols.
The course is arranged in a format that starts with the video lessons before the downloadable materials to help the learner in revision of the concepts taught.
The course is designed for parents whose children are still in high school, mathematics educators and anyone interested in geometry and problem solving.
This self-paced online course includes video lessons and a downloadable pdf note attached to each video. Approximately 2-3 hours, depending on the learners pace is required to cover the course.
Join us on this engaging journey into the world of similar triangles.