asa congruence

QR for lesson

I would like to guarantee that the following triangles are congruent.

Use whatever way you want to show if the triangles below are or are not congruent. Remember what methods you used.

1) On the back side draw a two inch line (use a pencil). 2) Draw two more lines to turn it into a triangle. 3) Compare you triangle with the people around you. Can you guarantee that everyone in the room will have the same triangle? 

Activity

Activity4) Erase everything except for your two inch line.  

5) Use the two inch line to create another line that will form a 30° angle. 6) Draw one more line to form a triangle 7) Compare you triangle with the people around you. Can you guarantee that everyone in the room will have the same triangle?

Activity8) Erase the line that is NOT part of the 30° 9) Use the other side of the two inch line two creates a 40° angle. Extend your line until they meet to form a triangle.  10) Compare you triangle with the people around you. Can you guarantee that everyone in the room will have the same triangle?

What do you notice?

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In order to show to triangles (or other figures) are congruent, you need to show ALL the corresponding segments from both figures are congruent and ALL the corresponding angles from both figures are congruent.

While doing this can get repetitive, there are ‘tricks’ to help show congruence. This is what we will study.

ASA CongruenceObjective: Use the ASA congruence relationship to write and justify triangle congruence.

DefinitionWhen I gave you a side length and two angles in between the side length, everyone should have created congruent triangles.

The reason is there is only ONE possible triangle that can be made where a side is two inches and the angle in between is 30 and 40 degrees.

ASA (Angle-Side-Angle) triangle congruence happens when two angles and the included side of one triangle is congruent to two angles and the included side of another triangle.

DiagramIn ΔABC:m<A = 30°m<C = 40°AC = 2’’

In ΔDEF:m<D = 30°m<F = 40°DF = 2’’

By applying ASA , ≅ ΔABC ≅ΔDEF

What additional information do you need in order to conclude that ΔMQP ≅ Δ NPQ? Explain your reasoning.

Goal: Show ASA relationship exists.

1) Both triangles share segment _______ • When two triangles share

the same exact segment or angle it is called the reflexive property.

2) For ASA to be true I need to show that:

1) <______ < ________≅2) <______ < ________≅

Example 1

What additional information do you need in order to conclude that ΔMQP ≅ Δ NPQ? Explain your reasoning.

How Mr.D. would answer this questions if it was a homework, quiz, or test question.

Since I know both triangles share segment QP, I would need to show that <MQP ≅< QPN and <MPQ ≅<PQN. This would allow me to say that ΔMQP ≅ Δ NPQ because of ASA ≅

Example 2Point T is the midpoint of segment SU. What additional information do you need in order to conclude that ΔRST ≅ Δ VUT? Explain your reasoning.

I know that segment _______ segment ≅______ because point T bisects segment SU.

I also know that <RTS <VTU because ≅they are __________ angles.

I would need to show that <RST <VUT. ≅That would show ΔRST ≅ Δ VUT because of ASA ≅

What additional information do you need in order to conclude that △SPR ≅△QRP? Explain your reasoning

Example 3 – You Try

Think About It Is there enough information in the diagram below to say that the two triangles are congruent? Explain you reasoning and draw a diagram to demonstrate.

No.Even though two angles and a side from both triangles are congruent, the triangle on the right shows ASA, while the triangle on the left does not. This is not enough to determine congruence.

HomeworkASA congruence in ebackpack. Do only #1-3

For full credit, make sure you completely explain your reasoning like we did in the examples.