1/8/14 1 Today you will need a pencil, ruler, protractor, one piece of patty paper, and one sheet of paper. Please get those ready before class begins. Today’s Objective: We will discover the Triangle Angle Sum Theorem and prove its conclusion. Common Core State Standard: G.CO.10a Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; Homework #2: Complete Geometry Lab 4-2 on page 222. Don't forget Try This ?'s 1-4. Also read Holt 4-2, pages 223-226. CC.9-12.G.CO.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. CC.9-12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CC.9-12.G.CO.10 Prove theorems about triangles. ◦ Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Transcript
1/8/14
1
Today you will need a pencil, ruler, protractor, one piece of patty paper, and one sheet of paper. Please get those ready before class begins.
} Today’s Objective: We will discover the Triangle Angle Sum Theorem and prove its conclusion.
} Common Core State Standard: G.CO.10a Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°;
} Homework #2: Complete Geometry Lab 4-2 on page 222. Don't forget Try This ?'s 1-4. Also read Holt 4-2, pages 223-226.
} CC.9-12.G.CO.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.
} CC.9-12.G.CO.8 Explain how the criteria for
triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
} CC.9-12.G.CO.10 Prove theorems about triangles. ◦ Theorems include: measures of interior angles of a triangle
sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
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2
} CC.9-12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding angles and the proportionality of all corresponding pairs of sides.
} CC.9-12.G.SRT.3 Use the properties of similarity
transformations to establish the AA criterion for two triangles to be similar.
} CC.9-12.G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
} CC.9-12.G.SRT.5 Use congruence and similarity criteria
for triangles to solve problems and prove relationships in geometric figures.
} CC.9-12.G.SRT.6 Understand that by similarity, side
ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
} CC.9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
} CC.9-12.G.SRT.9 (+) Derive the formula A=1/2ab
sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
} CC.9-12.G.C.3 Construct the inscribed and
circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
} CC.9-12.G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
} CC.9-12.G.GPE.7 Use coordinates to compute
perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
} CC.9-12.G.MG.1 Use geometric shapes, their
measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*
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} Draw and label ABC on a ½
sheet of notebook paper. ◦ Draw it pretty large. ◦ Label the angles
inside the triangle as well.
} On patty paper
draw a line ℓ and label a point P on the line.
A B
C } Use your ruler as a
tearing edge to tear out triangle ABC with straight lines.
} Carefully tear LARGE chunks of angles A, B, and C out.
} Place angles A, B, and C on your patty paper line.
} What is the sum of angles A, B, and C?
} Prove why that is the case!
} Given: ΔABC } Prove: m∠1 +
m∠2 + m∠3 = 180°
} Hint: You will need to draw an auxiliary line as I’ve shown you.
