Triangle Congruences

SSS SAS AAS ASA HL

Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

A Yes. CAB DAC B Yes. ABC ADC C Yes. ABC ACD

D No. There's not enough information.

What additional information will allow you to prove the triangles congruent by the HL Theorem?

A A E B 90m BCE

C AC DC

D AC BD

In triangle ACB, segment CD bisects angle ACB and segment CD is perpendicular to segment AB. Using the given information, which of the following most easily justifies that triangle ACD is congruent to triangle BCD?

a. HL c. AASb. ASA d. AAA

Right triangles ABC and DEF are shown below.

The two triangles can be proven congruent by the SSS triangle congruency theorem. Which is a step in that proof?

A BE BE B 90m ABC m DEF

C AB AC BC DE DF EF

D m A m ABC m C m D m DEF m F

Given: bisects AD BE

What additional information is needed to prove the triangles congruent by Angle-Angle-Side method?

A A D

B A E

C B E D B E

In the figure below, SA=UG and m GAS m AGU

Which triangles could you prove congruent by SAS?

A B C D

SGU UASSAR UGRSUR AGRSAG UGA

In the figure below, point X is the midpoint of .ABWhich statement, when added to the given information, is sufficient to prove that ?XAC XBD

A is isosceles with B C bisects D

ACX AC AXAX XBAB CDAB CD

In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?

A

B

C

D

Statements Reasons1. AB AC 1. Given2. BAD CAD 2. Given3. AD AD 3. Reflexive Property4. BAD CAD 4. ?

5. BD CD 5. ?

6. AD bisects BC 6. Def. of segment bisector

Supply the missing reasons below. Given: ;

Prove: bisects AB AC BAD CADAB BC

a. ASA; CPCTC

b. SSS; Reflexive Property

c. SAS; Reflexive Property

d. SAS; CPCTC