Name______________________
Period_______
Date___________
Constructing Congruent Triangles Modeling Activity
1. Use your protractor to draw a triangle ABC with angle measures. A  20, B  40, C  120
Compare your drawings with a neighbor. Did you both draw congruent triangles? Explain your answer:
(You will be using this triangle to construct other triangles so you want to make it large enough to be able to
properly measure and not too large that it won’t fit on the other pages in the provided space)
Activity 1: Construct a triangle that has all 3 sides congruent to the three sides of ABC
1. Use a straightedge to draw any line l and select a point D on the line.
2. Use a compass to construct DE on l such that DE  AB (measure AB with your compass, place compass
on D, draw an arc on l…label that intersection E)
3. Use your compass to measure AC, place your compass on D, then draw an arc above line l.
4. 3. Use your compass to measure BC, place your compass on E, then draw an arc above line l, where this arc
and the arc from 3 intersect, label this point F.
5. Draw DF and EF to form DEF
Use your protractor and compass to answer the following:
1. DE ___________ 2. FE _____________ 3. DF ____________
4. AB ___________ 5. CB _____________ 6. AC ____________
7. mD ___________ 8. mF _____________ 9. mE ____________
10. mA ___________ 11. mC _____________ 12. mB ___________
So, because each side of ABC is congruent to DEF _______________________
We call this the SSS postulate…
S__________S__________S___________
Activity 2: Construct a triangle in which two sides are congruent to two sides AC and AB of ABC and the
included angle is congruent to the included angle A in ABC .
1. Use a straightedge to draw any line m and select a point G on the line.
2. Use a compass to construct GH on m such that GH  AB (measure AB with your compass, place compass
on G, draw an arc on m…label that intersection H).
3. Use your compass to construct G , G  A .
a. place your compass on A
b. make an arc that intersects AB and BC .
Label those
intersection points x and y.
c. using the same compass setting put your compass on G and make an arc that intersects line m, label
that point of intersection z
d. go back to original triangle and with your compass measure the distance between x and y, using that
setting place your compass on z and make an arc to intersect the larger arc you drew in step c.
e. draw a line from G to the intersection from d.
4. Use your compass to measure AC, using that setting put your compass on G and make an arc that intersects
your line from 3. Label this intersection I.
5. Draw HI to complete GHI
Use your protractor and compass to answer the following:
1. GH ___________ 2. GI _____________ 3. mG ____________
4. AB ___________ 5. AC _____________ 6. mA ____________
7. IH ___________ 8. mI _____________ 9. mH ____________
10. CB ___________ 11. mC _____________ 12. mB ___________
So, because two sides AND the included angle of those sides of ABC are congruent to the corresponding
two sides AND the included angle of DEF _______________________
We call this the SAS postulate…
S__________A__________S___________
Activity 3: Construct a triangle in which two angles are congruent to two angles  A and  B of
congruent to the included side AB in
ABC and the included side is
ABC .
1. Use a straightedge to draw any line m and select a point J on the line.
2. Use a compass to construct JK on m such that JK
m…label that intersection K).
3. Use your compass to construct J , J  A .
a. place your compass on A
 AB (measure AB with your compass, place compass on J, draw an arc on
b. make an arc that intersects AB and BC . Label those intersection points x and y.
c. using the same compass setting put your compass on J and make an arc that intersects line m, label that point of
intersection z
d. go back to original triangle and with your compass measure the distance between x and y, using that setting place your
compass on z and make an arc to intersect the larger arc you drew in step c.
e. draw a line from J to the intersection from d.
4. Use your compass to construct K , K  B .
a. place your compass on B
b. make an arc that intersects AB and BC . Label those intersection points x and y.
c. using the same compass setting put your compass on K and make an arc that intersects line m, label that point of
intersection p
d. go back to original triangle and with your compass measure the distance between x and y, using that setting place your
compass on p and make an arc to intersect the larger arc you drew in step c.
e. draw a line from K to the intersection from d.
5. Label the point of intersection where the two new sides meet L.
1. mJ ___________ 2. mK _____________ 3. JK ____________
4. mA ___________ 5. mB ____________
6. AB ___________
7. mL ___________ 8. mC ____________
9. JK ___________ 10. JL ____________
So, because two angles AND the included side of those angles of ABC are congruent to the
corresponding two angles AND the included side of JKL _______________________
We call this the ASA postulate… A__________S__________A___________