Download Geometry Unit 2 Formative Items Part 1

Geometry Items to Support Formative Assessment
Unit 2: Triangles, Proof, and Similarity
Part A: Triangle Relationships, Congruence, and Proof
Prove geometric theorems.
G.CO.C.9 Prove theorems about lines and angles. Theorems include: points on a perpendicular
bisector of a line segment are exactly those equidistant from the segment’s endpoints.
G.CO.C.9 Task
Segment BD is the perpendicular bisector of segment AC. Prove that triangle ABC is an
isosceles triangle.
Solution:
Note: students could use proof blocks, write a paragraph, or use a two column proof. The two
column proof is shown below, but students do not have to use this method as long as they have
the same content shown in another method.
Statements
Reasons
Segment BD is the perpendicular bisector of
segment AC.
Given
Angle ADB and Angle CDB are right angles
Definition of perpendicular bisector
Angle ADB is congruent to Angle CDB
All right angles are congruent
Segment AD is congruent to Segment DC
Definition of perpendicular bisector
BD is congruent to BD
Reflexive Property
Triangle ADB is congruent to triangle CDB
SAS
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
AB is congruent to BC
CPCTC
Triangle ABC is an isosceles triangle
Two sides are congruent in any isosceles
triangle
G.CO.C.9 Item 1
Use the diagram below. Verify that the points on the perpendicular bisector are equidistant from
the endpoints A and B.
Solution:
Use a piece of patty paper, a straight edge, or CPCTC to confirm the distance AE is equal to the
distance BE. Repeat the process for points C, F, G.
G.CO.C.9 Item 2
What do you know about the two triangles created by the perpendicular bisector in the diagram
below? Explain your reasoning.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
Solution:
The points on the perpendicular bisector are equidistant from the endpoints. Therefore, the
corresponding sides are congruent. The perpendicular bisector creates right angles and is
congruent to itself. Therefore, the two triangles are right triangles.
Prove geometric theorems. (This standard will be embedded throughout this unit)
G.CO.C.10 Prove theorems about triangles. (Theorems include: 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.)
G.CO.C.10 Task
When your geometry teacher asked your class to prove that the base angles of an isosceles
triangle are congruent, one group created the poster shown below.
Several members of your group have questions about this group’s solution. How would you
explain each of these points to your group?
How do we know that line DC is the perpendicular bisector of segment AB?
How do we know that triangle ACD is congruent to triangle BCD?
Possible solution:
Since segment AC is congruent to segment BC we know that point C is on the perpendicular
bisector of segment AB. So line CD is the perpendicular bisector of segment AB.
Triangle ACD is congruent to triangle BCD by SSS.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.