Theorems invloving inequalities in a triangle
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The lesson aims to teach students about the properties of triangles, specifically focusing on identifying the largest and smallest angles based on side lengths and understanding inequalities in triangles. It includes a structured procedure involving awareness, motivation, presentation, and analysis of triangle properties, alongside practical activities for drawing and measuring. The lesson also emphasizes the importance of promoting equality and preventing inequalities in real-life scenarios.
Theorems invloving inequalities in a triangle
- 1. I. Objectives: At the end of the lesson, students are expected to: a. Name the largest and the smallest angle given the sides of a triangle; b. Arrange the sides of a triangle in order of increasing length given the angles; c. Cite ways to promote equality and prevent inequalities. II. Subject Matter: Theorems Involving Inequalities in a Triangle Reference: Mathematics Learners’ Module Grade 8 page (350-353) Skills: drawing, analyzing and solving Values: disadvantage of inequalities III. Materials: ruler, protractor, pintail pen, manila paper IV. Procedure: 5A’s Method Teacher’s Activity Students’ Activity A. Awareness a. Review Good morning class! (checking of attendance) (checking of assignment) What was our lesson last meeting? What is again HyL Congruence Theorem? How about the definition of HyA Congruence Theorem? Who can illustrate the HyL and HyA on the board? Very good! Good morning Sir! Our lesson last meeting was about HyL and HyA Congruence Theorem. HyL Congruence Theorem states that, “If the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and a leg of another triangle, then the triangles are congruent”. HyA Congruence Theorem states that “If the hypotenuse and an acute angle of one right triangle are congruent to the corresponding hypotenuse and an acute angle of another right triangle, then the two triangles are congruent”. Student does as told
- 2. b. Motivation In our previous discussions, we’ve discussed about postulates and theorems of congruence of triangles. Now class, what if the sides and angles of a triangle are not congruent, what do you think? Do you know class about certain theorems of inequalities in a triangle? c. Presentation So be with me this morning as I discuss to you about theorems involving inequalities in a triangle. d. Statement of the Aim *name the largest angle and smallest angle given the sides of a triangle; *arrange the sides of a triangle in order of increasing length given the angles; *describe the disadvantage of inequality. B. Activity I will group in to two groups. Let’s proceed to our activity. Let one student to draw the figure on the board Let another student to explain the figure on the board. (possible answer) No, Sir! Theorems involving Inequalities in a triangle Student does as told Student does as told Do the following in your group; 1. Use a ruler to draw a triangle named OPQ . 2. Make sure that OP is vertical which measures 15cm, PQ is horizontal which measures 20cm and OQ is diagonal which measures 25cm. 3. Use a protractor to measure the angles O, P and Q. 4. Indicate on the triangle OPQ the measures of the three sides and their opposite angles
- 3. C. Analysis What have observed about the sides of the ?OPQ How are you going to describe the three sides of ?OPQ How about the angles then? What is the shortest side? What is the smallest angle? Are the side OP and the angle Q opposite? So the smallest angle is opposite to the shortest side. What side is longer thanOP ? What angle is greater than Q ? Are the Q and PQ opposite? Then, how are you going to describe the longest side and the largest angles? I observed that the sides and angles of OPQ have different measures. The three sides of OPQ are not congruent. The three angles also are not congruent. The shortest side isOP . The smallest angle is Q ? They are opposite because they are facing each other. The side which is longer than OP is PQ ? The angle which is greater than Q is O . They are opposite because they are facing each other. The largest side OQ and the largest angle P are also opposite to each other. O P Q 530 370950 20cm 15cm 25cm
- 4. D. Abstraction How are you doing to conclude this triangle OPQ in terms of the inequalities of the sides and angles? Another hand! Very good! For your better understanding, here are two theorems which involve inequalities in a triangle. Everybody read and copy! Values Integration A while ago class we have discussed the inequalities in a triangle. Class, in connection to our real life situation how are you going to promote equality and to prevent inequality? Exactly! When the sides of a certain triangle are not congruent then the angles also are not congruent. When the sides of a certain triangle are not congruent then the opposite angles of those sides are also not congruent. If two sides of a triangle are not congruent, then the angles opposite these two sides are not congruent, and the larger angle is opposite the longer side. If two angles of a triangle are not congruent, then the sides opposite these two angles are not congruent, and the longer side is opposite the larger angle. I can promote equality and prevent inequality by being fair to everybody in everything that I do. Equality begins with being fair in just a simple action. Just like falling in line in a canteen, in withdraw machine, or even in the bank, those simple actions have great impacts on the society since to promote equality and at the same time to prevent inequality among people.
- 5. E. Application Activity 1 Directions: Name the largest and the smallest angle of the following triangles given the length of sides. 1. In ABC , 12AB , 16AC and 19BC 2. In DEF , 40DE , 35DF and 55FE 3. In GHI , 32GI , 50GH and 35HI 4. In JKL , 28JK , 40KL and 20JL 5. In MNO , 22MN , 38MO and 50NO V. Evaluation Directions: Arrange the sides of the following triangles in the order of increasing lengths given the measures of angles. 1. 2. ,B A ,D E ,I H ,J K ,M O , ,ED RD RE , ,ZY XY XZ 450 500 850 R E D 330 350 1150 X Z Y
- 6. 3. VI. Assignment Directions: Fill the blanks with the correct relation symbol (>,<) to show the relationship: 1.) between segments, and 2.) between angles in the corresponding figures: 1. ___ 2. ___ 3. ___ 4. ___ 5. ___ In SON m S m O m S m N m O m N m N m O m O m S , ,LS DS DL 1. 2. 3. 4. 5. 450 600 750 D L S O S N 25 45 56