Chapter Test
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Start by drawing the diagram. Then, consider the Transitive Property of Equality.
Example Diagram:
Proof: See solution.
We are asked to draw and label a diagram that represents the given information. Then, we will prove that the distance between the elephants and the giraffes is equal to the distance between the tigers and the zebras. We can choose any proof format, so we will write a two-column proof. Let's do it!
We know that all the animals are located along a straight walkaway. We are also told that the giraffes are halfway between the elephants and the lions. This means that the segment that connects the elephants and the giraffes has the same length as the segment that connects the giraffes and the lions. By the definition of congruent segments, these two segments are congruent.
Additionally, we know that the tigers are halfway between the lions and the zebras. Following the same reasoning as before, we know that the segment that connects the lions and the tigers is congruent to the segment that connects the tigers and the zebras.
Let's connect the two diagrams.
Now we will write a two-column proof showing that the distance between the elephants and the giraffes EG is equal to the distance between the tigers and the zebras TZ. EG? =TZ A two-column proof lists each statement on the left and its justification to its right. Each statement must follow logically from its previous steps. Let's use our diagram to write the proof. Here, we can identify three pairs of congruent segments. Statement1) & EG≅ GL, LT≅ TZ, & GL≅LT Reason1)& Given The definition of congruent segments tells us that the lengths of congruent segments are equal. Statement2) & EG=GL, LT=TZ, & GL=LT Reason2)& Definition of congruent segments We can use the Transitive Property of Equality to show that the distance between the elephants and the giraffes is equal to the distance between the lions and the tigers. EG= GL GL=LT ⇒ EG=LT This is our third statement. Statement3) & EG=LT Reason3)& Transitive Property of Equality Let's use this property once more. EG= LT LT=TZ ⇒ EG=TZ This is our fourth and last statement! Statement4) & EG=TZ Reason4)& Transitive Property of Equality We proved that EG=TZ, so we can now complete our two-column table.
Statements
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Reasons
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1. EG≅ GL, LT≅ TZ, GL≅ LT |
1. Given
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2. EG=GL, LT=TZ, GL=LT |
2. Definition of congruent segments
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3. GL=TZ
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3. Transitive Property of Equality
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4. EG=TZ
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4. Transitive Property of Equality
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