Complete the statement.
1. Isosceles triangle △ABC has congruent angles at B and C. If BC is bisected at D and AD is drawn, by the side, side, side triangle congruence postulate, ______________________.
A. △ADB≅△ADC
B. △ABC≅△ADC
C. △ADB≅△DCA
D. △ADB≅△ABC
2. Given △DEF with DE=DF and EF bisected at G, what can the side, side, side triangle congruence postulate be used to prove?
A. ∠DEF≅∠FDE
B. ∠DGF≅∠DFG
C. ∠DEF≅∠DFE
D. ∠DFE≅∠DGE
3. A right triangle, △JKL, is given with ∡KJL=30° and ∡JKL=90°. JM is drawn such that L, K, and M are collinear. Points J and M are joined by JM with JM=JL. Find ∡JML.
A. 30°
B. 90°
C. 180°
D. 60°
4. In the figure provided, precise measurements are given for the length of each side of △ABC.
If point D is on △ABC and AD is constructed, determine the statement that could be used to prove that ∡B=∡C.
A. Point D is on BC, such that BD=6.1 and BD=CD. Since AD≅AD by the side, side, side triangle congruence, △ABD≅△ACD and, therefore, ∠B≅∠C.
B. Point D is on AC such that CD=5.95 and DA=DC. Since DB≅DB by the side, side, side triangle congruence, △ADB≅△CDB and, therefore, ∠B≅∠C.
C. Point D is on AC such that AD=5.95 and AD=CD. Since BD≅BD by the side, side, side triangle congruence, △ABD≅△CBD and, therefore, ∠B≅∠C.
D. Point D is on AB such that AD=6.1 and AD=BD. Since CD≅CD by the side, side, side triangle congruence, △ACD≅△BCD and, therefore, ∠B≅∠C.
5. In the image provided, ⊙A has AD drawn through the center and intersecting CB at E.
Which of the following is not provided in the image above but is necessary in order to prove that ∠ABC≅∠ACB?
A. △ABC is isosceles.
B. AD=AB=AC
C. EC=EB
D. AB=AC
1. A. △ADB≅△ADC
2. C. ∠DEF≅∠DFE
3. D. 60°
4. C. Point D is on AC such that AD=5.95 and AD=CD. Since BD≅BD by the side, side, side triangle congruence, △ABD≅△CBD and, therefore, ∠B≅∠C.
5. A. △ABC is isosceles.