1.4 Congruent Triangles
Triangle Sums
Pacing:This lesson should take one class period
Goal:The purpose of this lesson is to familiarize students with the polygonal sum theorem and its specific applica-
tion, the triangle sum theorem. Students will incorporate algebra to find unknown polygons given an interior angle
sum and find an interior angle sum given a specific polygon.
Physical Models!Using the triangle from the introduction, have students measure the interior angles of the triangle.
Then, by extending segmentsAB,BC,AC, students see three new exterior angles and should measure these too.
Students should make the connection that the interior and exterior angles form a linear pair, and by the Linear Pair
Theorem, are supplementary.
Extension!The Triangle Sum Theorem is a special case of the Polygonal Sum Theorem, in which the sum of interior
angles of ann−gon is found by the following formula:
T= 180 (n− 2 ), wheren≥ 3
Ask students to brainstorm the reasoning behindn≥3.Students should remember that a polygon cannot be formed
with less than three segments.
Physical Model!To demonstrate the explanation of the Triangle Sum Theorem found on page 209, students should
draw a triangle and measure all three interior angles. Students can then rip or cut off any two angles and, like a
puzzle, fit them with the third. The result is a straight line with a measurement of 180 degrees.
Technology Activity!Using a geometric software program, have students follow these steps:
a. Place 3 noncollinear points on the plane, labeledA,B,C. Connect these three points to form 4 ABC.
b. Compute the measures of^6 A,^6 B,^6 C. How can we classify this triangle? Is it scalene, equilateral, or
isosceles? Is it acute, obtuse, or right?
c. Find the sum of all three angles.It should equal180 degrees.
d. Highlight pointsA,B(thusAB), and pointC. Using the appropriate menu, click on “construct a parallel line.”
There should a line parallel toAB.
e. Locate points on the line parallel toAB, calling themFandE.
f. Measure^6 ABFand^6 CBE. Calculate the sum of these two angles and^6 A.The sum should equal180 degrees.Congruent Figures
Pacing:This lesson should take one class period
Goal:The goal of this lesson is to prepare students for the five triangle congruency theorems: Angle-side-angle,
side-angle-side, side-side-side, angle-angle-side, and the special case of side-side-angle, the hypotenuse-leg theorem.
This lesson provides a needed introduction by looking at congruent triangles in a non-formal manner.
Notation, Notation, Notation!Revisit congruence notation from earlier lessons:∼=Stress the importance of labeling
each congruency statement such that the congruent vertices match. For example,ABCD∼=LMPQshows^6 A∼=
Chapter 1. Geometry TE - Teaching Tips