Foundations of Math III
Unit 4: Logical Reasoning (Part 2)
in Geometry
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1.12 Practice Making Mini-Proofs
Fill in the missing pieces for each mini-proof.
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1.13Homework - Triangle Congruence Theorems
Determine which theorem can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
Flow Proof Examples
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1.14 Homework - Triangle Congruence Theorems
Determine which theorem can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
State what additional pair of angles or sides need to be congruent order to prove that the triangles congruent using the given theorem.
7. Fill in the blanks in the following flow proof.
1.15 Examples – Flow Proofs using CPCTC
Example 1
Hutchins Lake is a long, narrow lake. Its length is represented by in the diagram shown below. Dmitri designed the following method to determine its length. First, he paced off and measured and . Then, using a transit, he made . He then marked point D on so that , and he measured. Dmitri claims that . Is he correct? Justify your answer.
Example 2
To measure the width of a sinkhole on his property, Harry marked off congruent triangles as shown in the diagram. He then measures the length of to find the length of . How does he know that the lengths of and are equal? Justify your answer.
Example 3
Given:with . An auxiliary line is drawn from vertex H to the midpoint N of to form two triangles.
Prove:
1.15 Homework – Flow Proofs using CPCTC
1) According to legend, on of Napoleon’s officers used congruent triangles to estimate the width of a river. On the riverbank, the officer stood up straight and lowered the visor of his cap until the farthest thing he could see was the edge of the opposite bank (Point F). He then turned and noted the spot on his side of the river that was in line with his eye and the tip of his visor (Point G). The officer then paced off the distance along the riverbank from where he was standing to the spot he sighted (EG). He declared that distance to be the same as the width of the river. Prove that he was correct.
Given: are right angles (We assume that the officer was standing perpendicular to the ground)
(because he sighted both points F and G from the same angle)
Prove:
Fill in the empty spots in the flow proof below.
Fill in the missing reasons or statements in each proof.
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1.16 Warm Up
1.16 Review for Quiz
For each example, determine which triangle congruence postulate is needed to prove the two triangles are congruent. Then write the congruence statement.
Complete the following flow proof.
1.17Warm Up – Missing Parts
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