a Which vertices are corresponding given the congruence statement?
B
b DG and TP are corresponding sides.
A
aExample sketch:
B
b y=7
Practice makes perfect
a Let's first draw three lines that are 14, 18 and 21 units.
To construct our triangles, we need to use a compass. However, first we will match correct sides with each other by using the congruence statement.
△ T A P ≅ △ D O G
⇓
T A ≅ D O, A P ≅ O G, T P ≅ D G
Open the compass to the width of, for example, the segment that is 21 units long, and draw TP and DG.
Next, we want to draw a second side. Let's measure the side that's 18 and then draw two arcs, one around P and the other around D.
Let's also measure the final side and draw a second pair of arcs around T and G.
By drawing segments from the endpoints of TP and DG and to either point of intersection of the two arcs, we can create our congruent triangles.
b We know that DG=2y+7. From Part A, we also know that DG is 21 units. With this information, we can write an equation because corresponding sides of congruent triangles are equal in length.
