Week-2-Bernardo.pptx
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This document outlines a geometry lesson on various theorems including the midline theorem, midsegment theorem of trapezoids, theorems on isosceles trapezoids, and theorems on kites. It includes learning activities to help students understand and apply these theorems, such as using a scavenger hunt, cutting and reconnecting shapes, and solving practice problems. The overall learning objectives are for students to be able to prove and apply these different geometry theorems.
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This document is a presentation about triangles created by Manish Raj Anand, a 10th grade student at The Doon Global School. It contains information about different types of triangles, including equilateral, isosceles, and scalene triangles. It discusses triangle properties such as angles, sides, perpendicular bisectors, medians, altitudes, the circumcenter, and the triangle inequality. The presentation was created using information found online and pictures collected from the internet.
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The document discusses different types of proofs in geometry using concepts like congruence, similarity, triangles, and parallel lines. It provides examples and definitions of key terms and asks multiple choice questions to test understanding. To prove congruence, one must observe that all internal angles are the same and all angles and sides correspond. Similar shapes differ in that their lengths may be different, while congruent shapes have exactly matching side lengths and angles.
Quadrilaterals
This document provides information about various types of quadrilaterals (four-sided shapes). It defines quadrilateral, rectangle, rhombus, square, parallelogram, and trapezium. For each shape, it describes the key properties like side lengths, angle measures, and how to calculate the area and perimeter. The goal is to explain these geometric concepts in a clear, step-by-step manner to make mathematics more accessible and enjoyable for students.
Triangles
1) A triangle is a three-sided polygon with three vertices and three edges.
2) Triangles can be classified based on side lengths (equilateral, isosceles, scalene) or interior angles (right, acute, obtuse).
3) The interior angles of any triangle always sum to 180 degrees. Congruent triangles have the same shape and size, while similar triangles have the same angle measures but sides proportional in length.
P
Here are the key points in the example:
1. The triangles ΔCAT and ΔDOG are placed on top of each other so that their vertices coincide or overlap.
2. This establishes a correspondence between the parts of the two triangles.
3. Since the vertices coincide, the corresponding sides and angles also coincide.
4. Triangles with coinciding corresponding parts are said to be congruent.
5. The congruence of the two triangles is symbolized as ΔCAT ≅ ΔDOG.
Geom 5point3and4
- The three medians of a triangle intersect at the centroid, which is located 2/3 of the distance from each vertex to the midpoint of the opposite side.
- The three altitudes of a triangle are concurrent at the orthocenter, which can lie inside, on, or outside the triangle depending on whether the triangle is acute, right, or obtuse.
- A midsegment connects the midpoints of two sides of a triangle. The midsegment is parallel to the third side and is half as long based on the Midsegment Theorem.
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- 1. Good Day! I can’t wait to learn with you.
- 2. SCAVENGER HUNT Find something that… is BLUE.
- 3. SCAVENGER HUNT Find something that… has RIGHT ANGLES.
- 4. SCAVENGER HUNT Find something that… has FOUR SIDES.
- 5. Midline Theorem Midsegment Theorem of Trapezoid Theorems on Isosceles Trapezoid Theorems on Kite
- 6. Learning Outcomes At the end of the lesson, the learners are able to: 1. Prove the Midline Theorem; 2. Prove the midsegment theorem on Trapezoids; 3. Prove theorem on Isosceles Trapezoids; 4. Prove theorem on Kites; and 5. Apply the midline theorem, and theorems on trapezoids and kites in solving a problem.
- 7. It’s Parallelogram! Draw an isosceles triangle. A C B
- 8. It’s Parallelogram! Choose a third side of a triangle. Mark each midpoint of the other two sides then connect the midpoints to form a segment. Does the segment drawn look parallel to the third side you chose? YES A C B 2 3 1
- 9. It’s Parallelogram! Measure the segment drawn and the third side you chose. Compare the length of the segment drawn and the third side you chose. What did you observe? The midsegment is half the length of the third side and two sides are parallel. 2 u 4 u A D E C B
- 10. It’s Parallelogram! Cut the triangle along the segment drawn. What two figures are formed after cutting the triangle along the segment drawn? Isosceles Trapezoid and A D E C B
- 11. It’s Parallelogram! Reconnect the triangle with other figure in such a way that their common vertex was midpoint and that congruent segments formed by a midpoint coincide. After reconnecting the cutouts, what new figure is formed? Parallelogram D E A C B
- 12. The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half as long. Midline Theorem
- 14. The segment joining the midpoints of the legs of a trapezoid is called median. The median of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. Midsegment Theorem of Trapezoid
- 16. There are three theorems related to isosceles trapezoids as follows: 1. The base angles of an isosceles trapezoid are congruent. 2. Opposite angles of an isosceles trapezoid are supplementary. 3. The diagonals of an isosceles trapezoid are congruent. Theorems on Isosceles Trapezoid
- 18. There are two theorems related to kites as follows: 1. In a kite, the perpendicular bisector of a least one diagonal is the other diagonal. 2. The area of a kite is half the product of the lengths of its diagonals. Theorems on Kite
- 20. GO FOR IT! LEARNING TASK Instructions: Consider each given information and answer the questions that follow.
- 24. ASSIGNMENT Advance study on the fundamental theorems of proportionality.
- 25. Summary 1. The Midline Theorem 2. The midsegment theorem on Trapezoids 3. Theorem on Isosceles Trapezoids 4. Theorem on Kites; and 5. Apply the midline theorem, and theorems on trapezoids and kites in solving a problem