Download HW 31 overlapping triangles

Geometry
Overlapping Triangles
Name: ____________________
In each diagram, the stated triangles are congruent. Identify their
common side or angle.
1. BAE  ABC
2. SUV  WUT
Separate and redraw the indicated triangles. Identify any
common angles or sides.
3. ACF and AEB
4. FKJ and HJK
To start, redraw each triangle separately. Then
mark parts congruent that you know are
congruent.
Complete the drawing to
separate the triangles. Then
mark parts congruent as before.
For 5&6, separate and re-draw the triangles given. Use the given information to mark
your separated triangle diagram. Remember overlapping sides/angles. Then, decide if
you can justify the congruence statement.
5.
∆𝑈𝑋𝑊:
∆𝑉𝑊𝑋:
̅̅̅̅, ∠𝑼𝑿𝑾 ≅ ∠𝑽𝑾𝑿
Given: ̅̅̅̅̅
𝑼𝑾 ≅ 𝑽𝑿
Can you justify ∆𝑼𝑿𝑾 ≅ ∆𝑽𝑾𝑿 ?
If yes, what is your justification?
YES
NO
6.
∆𝐾𝐽𝑁:
∆𝐾𝐿𝑀:
̅̅̅̅ ≅ ̅̅̅̅
Given: 𝑲𝑱
𝑲𝑳, ̅̅̅̅̅
𝑲𝑵 ≅ ̅̅̅̅̅
𝑲𝑴
Can you justify ∆𝑲𝑱𝑵 ≅ ∆𝑲𝑳𝑴 ?
YES
NO
If yes, what is your justification?
Draw the diagram described.
7. Draw a line segment on your paper. Then draw two overlapping, congruent
triangles that share the segment as a common side.
8. Draw two right triangles that share a common angle that is not a right angle.