Topic: Finding Unknown angles
Key Vocabulary: 1. Supplementary Angles : Two Angles are Supplementary when they add up to 180 degrees.
2. Complementary angles: Two Angles are Complementary when they add up to 90 degrees (a Right Angle).
3. Vertical angles: Vertical Angles are the angles opposite each other when two lines cross. They are always equal.
4. Adjacent Angles: Two Angles are Adjacent when they have a common side and a common vertex (corner point), and don’t overlap.
Prior Knowledge: Students should already have a clear idea about ( Acute, Obtuse, Reflex) angles and their measurement. In addition, they should also have had clear idea about the parts of a angle such as (The corner point of an angle is called the vertex) and ( the two straight sides are called arms) and how to give the angle a name, such as ABC or CBD
1.key vocabulary : Location Shape Angle distance Pre-image image Transformation Translation Rotation Reflection Clockwise Counterclockwise
2.Prior knowledge : Recall the definition of congruence
3.Focus idea or questions
a. How do you identify translation, reflection and rotation?
b.What are the common attributes among translations, rotations and reflections?
c.What are the differences between them?
Topic : Congruence
Learning Objective: Proving Triangles Congruent.
- Students will be able to prove triangles are congruent using ASA, SAS, and SS.
- Students will be able to prove triangles are congruent using definitions of midpoint and bisector.
- Student will be able to write basic formal proofs of triangle congruence.
Common Core State Standard High School G-CO.8
Understand congruence in terms of rigid motions
- Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
- Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
- Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Topic: Angle Side Angle
Learning Objective: students will be able to determine the congruence between triangles when given two angles and it’s included side for various triangles
Students will be able to state the Angle Side Angle postulate.
Common Core Standard: CCSS.Math.Content.HSG.CO.B.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Key Vocabulary: Angle-Side-Angle postulate
Prior Knowledge: SAS postulate, SSS postulate, Corresponding Side, Corresponding Angle, Congruence.
Topic: Exterior Angle Theorem
- The students will be able to explain verbally and in writing the relation between the exterior and the interior angles of the triangle
- the students will be able to find the measurement of the exterior angle of the triangle or one of the interior angles.
CCSS Standards: 8.G.5
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
Instructional resources and materials: smart board and computer with Geogebra.
key vocabulary: exterior angle, interior angle.
- the students should be familiar with straight angle and it’s measurement, and supplementary angles.
- the students should know the total measurements of the interior angles of the triangle.
focus idea or questions: what is the relationship between the exterior and the interior angles of the triangle.
introduction/ motivation: students should be able to find the measurement of the exterior angle of the triangle.
two problems are given to the students.
- find the measurement of angle A in the triangle abc with angle B = 50, angle C = 70?
- find the measurement of the
time estimate: 10 minutes
instructional strategies and learning activities: Geogebra sheet is given to the students.
practice: the students have to follow the instruction in the Geogebra sheet.
closure: the students are given an exit slip with one question to reflect on how helpful was Geogebra in understanding how the exterior angle and the interior angle are related.
- Topic: Pythagorean Theorem
- Learning Objective:
Students will be able to prove the Pythagorean Theorem
Students will be able to identify and apply the Pythagorean Theorem to find the missing length of a triangle
Students will understand when to apply Pythagorean Theorem
- Common Core State Standards:
8. G.6 – Explain a proof of the Pythagorean Theorem and its converse
8. G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions
Justin James Meyer
1- Students will know the formulas for finding the volume of cones and cylinders.
2- Students will understand how the volume of a cone is related to the volume of a cylinder.
3- Students will be able to recognize combinations of cones and cylinders.
4 -Students will be able to find the volume of 3 dimensional shapes combined from cones and cylinders.
Common Core Standards
8.G.9- Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Topic: Determining the angles between transversal and parallel lines.
- Students will identify the relationship between angles formed by two parallel lines and a non-perpendicular transversal.
- Students will be able to use theorems and postulates to determine the congruence and values of angles formed by two parallel lines and a non-perpendicular transversal.
- Students will use algebra and solve equations to find the measure of angles from the transversal.
- Students will be able to convey their reasoning orally and in writting.
Common Core State Standards:
Understand congruence and similarity using physical models, transparencies, or geometry software.
- Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
1.Corresponding Angles Postulate
- Alternate Exterior Angles Theorem
- Alternate Interior Angles Theorem
- Consecutive Interior Angles Theorem
- Consecutive Exterior Angles Theorem
- Vertical Angles Theorem
- Angle Relationships such as complementary, supplementary, adjacent, vertical, alternate interior, alternate exterior, corresponding, consecutive interior, and consecutive exterior.
- Solving one variable equations
Do now (5 mins to complete and 5 mins to go over): Identify the given angle relationships
Mini Lesson (20 – 25 mins): Describe all theorems and postulates with examples.
Activity (20 – 25 mins): Worksheet with problems progressing from easy to difficult that requires students to solve for the unknown angles when parallel lines are cut by a transversal. Students must give reasoning behind why they can say the value is equal to what they say it is (identify Theorems and Postulates present).
Exit ticket: Hand in activity worksheet.
Topic: Finding Unknown Angles
Learning objectives: Students will be able to use supplementary, complementary, vertical, and adjacent angles to find unknown angles .In addition, they will be able to use facts ( such as the measurement of the supplementary , complementary, vertical, and adjacent) angles to solve multi steps problem ( that require students to do several steps for example finding X , students will need to do these steps 1. adding two angles together. 2. Subtracting them from the angle measurement in order to find to fix the measurement of X) and to solve simple equations for unknown angle in a figure ( find the X angle in the figure for example (x+30=90).
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure.
Learning Objection: Students are able to identify and find the arc length and area of sector of circle.
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