CO_1 Median of a Trapezoid (3rd quarter).pptx
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This document discusses the median theorem of trapezoids. It begins by stating the objectives of drawing and labeling a trapezoid diagram, proving the median theorem, and collaborating with peers. It then provides examples of identifying different polygons based on their properties. The main content explains that the median of a trapezoid is parallel to the bases and its length is half the sum of the base lengths. It includes an example of using the theorem to find the length of a trapezoid's median. Students are asked to practice applying the theorem in additional examples.
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2) Key properties of parallelograms are reviewed, including opposite sides being congruent and parallel, opposite angles being congruent, and diagonals bisecting each other.
3) For a learning task, students are instructed to draw and measure a parallelogram, then make conjectures about measurements and properties.
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
- A trapezoid is a quadrilateral with one pair of parallel sides called the bases. The non-parallel sides are called the legs.
- An isosceles trapezoid has one pair of parallel sides and one pair of congruent non-parallel sides called legs.
- Theorems about the isosceles trapezoid include: the base angles are congruent, opposite angles are supplementary, and the diagonals are congruent.
- The median of any trapezoid is parallel to the bases and is equal to half the sum of the bases.
DLL3 MATH 9 WEEK 7.docx
This document is a daily lesson log for a 9th grade mathematics class taught by Angela Camille P. Cariaga from April 3-7, 2023. The lesson focused on the key concepts of quadrilaterals and triangle similarity. Students learned to investigate, analyze, and solve problems involving quadrilaterals and triangle similarity. Throughout the week, students illustrated similarity of figures, reviewed and continued learning about similarity of polygons and figures, and took a quiz. Activities included observing similar figures, solving proportions, drawing similar shapes, and identifying examples of similarity in daily life. The lesson aimed to help students understand that two polygons are similar if their corresponding angles are congruent and corresponding sides are proportional.
TRIANGLE-MIDLINE-THEOREM-TRAPEZOID-KITE.pdf
1. The document provides definitions and theorems related to geometric shapes including triangles, trapezoids, kites, and parallelograms. It defines key terms like midline, median, diagonal, and congruent sides.
2. Theorems covered include the triangle midline theorem stating the midline is parallel to the third side and half its length. For trapezoids, the midsegment theorem states the median is parallel to the bases and half their sum.
3. Theorems for kites include the diagonals being perpendicular and one diagonal bisecting the other or bisecting a pair of opposite angles.
G9Lesson 3_ The Trapezoid and its Properties.pptx
This document defines properties of trapezoids and isosceles trapezoids. It provides examples of using these properties to solve problems. A trapezoid has one pair of parallel sides called bases and two nonparallel sides called legs. An isosceles trapezoid has congruent legs. The median of any trapezoid connects the midpoints of the legs and is parallel to the bases, with length equal to half the sum of the base lengths. Worked examples demonstrate using properties of trapezoids and isosceles trapezoids to find missing side lengths and angle measures.
Geometry mell2010
1) The document discusses van Hiele levels of geometric reasoning, which describe how students develop understanding of geometry concepts through sequential levels of learning.
2) It provides details on the five van Hiele levels - visualization, analysis, abstraction, deduction, and rigor - and examples of the types of thinking associated with each level.
3) Activities are presented that involve organizing shapes, constructing geometric figures without tools, and investigating properties of triangles to help students advance through the van Hiele levels.
Leg Leg Congruence Theorem and LEg Acute angle Congruence Theorem
The document provides classroom rules and instructions for a geometry lesson on right triangle congruence theorems. It includes 4 classroom rules, instructions for a warm-up activity identifying geometric terms, objectives for the lesson, explanations of the Leg-Leg and Leg-Acute Angle Congruence Theorems with examples, and guide questions. It also describes scenarios of students applying the theorems to prove congruent right triangles and creating a wall décor using right triangle patterns.
chapter 6, triangles
This document provides an overview of triangles, including their properties, types, similarity, areas of similar triangles, and the Pythagorean theorem. It defines triangles as polygons with three sides and angles, and notes their interior angles sum to 180 degrees. Triangles are classified by angle and side length into right, acute, obtuse, isosceles, equilateral, and scalene varieties. Similarity is discussed, along with criteria like equal angles and proportional sides. Areas of similar triangles are shown to be proportional to a ratio of corresponding sides. Finally, the Pythagorean theorem and its applications to find missing sides of right triangles are covered.
6 1 coordinate proofs
Analytic geometry uses algebraic methods to study and prove geometric problems using coordinates. This chapter discusses using coordinate proofs to prove theorems from geometry. It provides instructions on how to construct a coordinate proof by drawing and labeling a diagram, listing given information, stating what will be proved, using algebra to add to the diagram and prove the statement, and writing a conclusion. Common algebraic methods used in proofs include the distance formula, identifying parallel and perpendicular lines, and finding midpoints. Examples provided are proving properties of right triangles, trapezoids, and triangles.
parallelogram story Dancayra rosario
Dancayra Rosario is a 15-year-old student completing a geometry project for their teacher Ms. Bush on the properties of rectangles. Rectangles have four sides with two pairs of equal length sides. They also have four right angles and diagonals that bisect each other. The document provides examples of how rectangles are similar to parallelograms due to having four sides and angles that add up to 360 degrees. It also explains how rectangles differ from other quadrilaterals through having adjacent equal angles. The document solves a perimeter problem for a rectangular pool to find its width.
Inovative lesson
1. The document presents a lesson plan for teaching students how to calculate the area of a trapezium.
2. It defines a trapezium as a quadrilateral with one pair of parallel sides and provides the formula to calculate the area as half the product of the distance between the parallel sides and the sum of the lengths of the parallel sides.
3. The lesson plan outlines checking prior knowledge, presenting a model and example calculation, having students derive the formula, and providing practice problems for students to apply the formula to find the area of different trapeziums.
Spelling challenge 4 Mathematics
This document provides spelling and vocabulary words related to math for a weekly spelling challenge, along with their definitions and examples of use in sentences. There are 10 math-related words to be learned for the week, including graph, ratio, rotation, pyramid, calculator, algebra, cylinder, protractor, compass, and trigonometry. Students are encouraged to use the new words in their lessons that week and help their peers achieve a score of 10/10 on the weekly spelling challenge.
Chapter 6, triangles For Grade -10
This document provides an overview of triangles, including their properties, types, similarity, areas of similar triangles, and Pythagorean theorem. It defines triangles as polygons with three sides and angles, and notes the angle sum property. Triangles are classified by angle and side length into right, obtuse, acute, isosceles, equilateral, and scalene varieties. Similarity is discussed, along with criteria like equal angles and proportional sides. Areas of similar triangles are directly proportional to a scale factor. Finally, the Pythagorean theorem and its applications to find missing sides of right triangles are covered.
G6 m5-a-lesson 3-t
This lesson teaches students how to calculate the area of acute triangles using the height and base. Students first decompose acute triangles into right triangles by drawing the altitude, and calculate the area of each right triangle. They then realize the total area is the sum of the right triangle areas. Finally, students learn that for any acute triangle, the area can be calculated as A = 1/2 x base x height, where the height is the altitude perpendicular to the base. Through examples, students verify this formula works for both decomposing triangles into right triangles and calculating the area directly.
Geometric Proofs
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.
Pramod
This document outlines a lesson plan for teaching students how to calculate the area of a parallelogram. It includes the learning objectives, which are for students to understand that the area of a parallelogram can be calculated as the product of one of its side lengths and its corresponding height. The lesson plan involves showing students models of parallelograms, having them draw diagonals and calculate triangle areas, and ultimately teaching them the formula that the area of a parallelogram is equal to base times height (A=bh). Examples are worked through to demonstrate how to apply this formula to find the numerical area of different parallelograms.
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CO_1 Median of a Trapezoid (3rd quarter).pptx
- 5. Objectives: a. draw a diagram of the trapezoid and label its bases, height and median based on the given the dimensions. b. prove the median theorem of trapezoid. c. work collaboratively with their peer/partner to solve mathematical problems and engage in productive discussions.
- 6. ACTIVITY
- 7. Who am I? Directions: Guess the polygon that is being describe by the statements.
- 8. I am a polygon. I have three sides. I have three interior angles. I am TRIANGLE!
- 9. I am a polygon. I am a quadrilateral. I have four right angles. I have two congruent diagonals. I have two diagonals that bisect each other. I have two pairs of opposite sides that are congruent and parallel. I am RECTANGLE!
- 10. I am a polygon. I am a quadrilateral. I am a parallelogram. I have two diagonals that bisect each other. I have two pairs of opposites that are parallel. I have two diagonals that are perpendicular to each other. I am RHOMBUS!
- 11. I am a polygon. I am a quadrilateral. I have four equal sides. I have two congruent diagonals. I have two diagonals that bisect each other. I have two diagonals that are perpendicular to each other I am SQUARE!
- 12. What a TRAP! Do the procedure below and answer the questions that follow. 1. Draw trapezoid TRAP where 𝑇𝑃 ⊥ 𝑃𝐴, 𝑇𝑅 = 4 𝑐𝑚, 𝑇𝑃 = 5 𝑐𝑚, 𝑎𝑛𝑑 𝑃𝐴 = 8𝑐𝑚 2. Name the midpoints of TP and RA as G and O, respectively. 3. Connect G and O to form a segment.
- 14. Guide Questions a. What are the names of the bases of trapezoid TRAP? b. What are the names of the legs of the trapezoid TRAP? c. Does 𝐺𝑂 look parallel to the bases of the trapezoid? d. Measure 𝐺𝑂. How long is it? e. What is the sum of the bases of TRAP? f. Compare the sum of the bases and the length of 𝐺𝑂. What did you find? g. Make a conjecture about the sum of the bases and the length of the segment joined by the midpoints of the legs. Explain your answer.
- 15. Median of a Trapezoid The line segment joining the midpoints of the legs of a trapezoid is called median. The previous activity helped you discover the following theorem about the median of a trapezoid: Theorem 6: The median of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
- 16. SHOW ME! Given: Trapezoid MINS with median 𝑇𝑅 Prove: 𝑇𝑅 ∥ 𝐼𝑁, 𝑇𝑅 ∥ 𝑀𝑆 𝑇𝑅 = 1 2 𝑀𝑆 + 𝐼𝑁
- 17. Example: Given trapezoid NICE with median 𝐴𝐵, find the measure of 𝐴𝐵. Solution: 𝐴𝐵 = 1 2 𝑁𝐼 + 𝐸𝐶 𝐴𝐵 = 1 2 12 𝑐𝑚 + 48 𝑐𝑚 𝐴𝐵 = 1 2 60 𝑐𝑚 𝐴𝐵 = 30 𝑐𝑚
- 18. Try this.! Given trapezoid HETO with median RC. If 𝐻𝐸 = 15 𝑐𝑚 and 𝑂𝑇 = 27 𝑐𝑚. What is the measure of 𝑅𝐶? Solution: 𝑅𝐶 = 1 2 𝐻𝐸 + 𝑂𝑇 𝑅𝐶 = 1 2 15 𝑐𝑚 + 27𝑐𝑚 𝑅𝐶 = 1 2 42 𝑐𝑚 𝑅𝐶 = 21 𝑐𝑚
- 20. Answer the following on your notebook. Given Trapezoid ABCD below. Identify the following 1. Legs ___________ and ____________ 2. Bases ___________ and ____________ 3. Median ___________ Using the same figure. 4. If 𝐵𝐶 = 20 cm, then 𝐴𝐷 = 30 cm, then 𝐸𝐹 = _________ 5. If BC = 12 cm, then 𝐸𝐹 = 18 cm, then 𝐴𝐷 = _________
Editor's Notes
- What is the definition of the base of a trapezoid? How about the legs of the trapezoid? Does segment GO looks similar to the Midline of a Triangle?
- To prove the theorem, students will do the activity SHOW ME!