a Follow the instructions you are given in the book.
B
b Use a protractor to measure appropriate angles, and record the results in a table.
C
c What can you say about the angles of triangles looking at the table you made in the previous part?
A
a See solution.
B
b See solution.
C
c If an altitude in a right triangle is drawn from a right angle, then it divides this triangle into two triangles that are similar to the original one.
Practice makes perfect
a First, we are asked to draw △ ABC with the right angle at vertex B and an altitude BD.
Next, we will draw two more right triangles MNP and WXY with the right angles at vertices N and X respectively. In each triangle we will draw its altitude from its right angle.
b In this part we are asked to measure and record the indicated angles. To do this, we will use a protractor. Let's start with △ ABC.
We can measure the rest of the angles in the same way.
Now we can complete the table using the angle measures we found.
Angle Measures
△ ABC
△ ABC
△ BDC
△ ADB
ABC
90^(∘)
BDC
90^(∘)
ADB
90^(∘)
A
45^(∘)
CBD
45^(∘)
BAD
45^(∘)
C
45^(∘)
DCB
45^(∘)
DBA
45^(∘)
△ MNP
△ MNP
△ NQP
△ MQN
MNP
90^(∘)
NQP
90^(∘)
MQN
90^(∘)
M
52^(∘)
PNQ
52^(∘)
NMQ
52^(∘)
P
38^(∘)
QPN
38^(∘)
QNM
38^(∘)
△ WXY
△ WXY
△ WZX
△ XZY
WXY
90^(∘)
WZX
90^(∘)
XZY
90^(∘)
W
60^(∘)
XWZ
60^(∘)
YXZ
60^(∘)
Y
30^(∘)
ZXW
30^(∘)
ZYX
30^(∘)
c Looking at the table we made in Part B, we can see that all three triangles in each row are similar by the Angle-Angle Similarity Theorem. Therefore, we can assume that if an altitude in a right triangle is drawn from a right angle, then it divides this triangle into two triangles that are similar to the original one.
