Preparing for the Regents Examination Geometry, AK

14 1. ___
DF ___
FE
2. 2 3
3. 1 4
4. ADF CEF (Linear pairs of congruent
angles)
5. ADF CEF (ASA ASA)
6. A C (CPCTC)
7. ABC is an isosceles triangle. (Definition
of an isosceles triangle)
15 1. ______
AEDC
2. 1 2
3. ___
BE ___
BD
4. AEB CDB
5. ___
AE ___
DC
6. ABE CDB (ASA ASA)
7. A C (CPCTC)
8. ABC is an isosceles triangle. (Definition
of an isosceles triangle)
9-8 Proving Right Triangles
Congruent by Hypotenuse-
Leg; Concurrence of Angle
Bisectors of a Triangle
(pages 207–208)
1 (a)
2 (d)
3 (c)
4 (b)
5 (a)
6 m1 24, m2 52, m3 104,
m4 52, m5 14, m6 114,
m7 14, m8 24, m9 142
Note: Since there are many variations of proofs,
the following is simply one set of acceptable
statements to complete each proof. Depending
on the textbook used, the wording and format
of reasons may differ, so they have not been
supplied for the method of congruence applied
in each problem. (These solutions are intended
to be used as a guide—other possible solutions
may vary.)
7 1. ___
SQ ___
PR
2. ___
SA ___
PB
3. SQP and SAP are right angles.
4. SQP and SAP are right triangles.
SP ___
SP
5. ___
6. ___
SQ ___
SA
7. SQP SAP (HL HL)
8. SPQ APS (CPCTC)
9. ___
PT bisects RPB. (Definition of
angle bisector)
8 1. ___
AE ___
BC
2. ___
CD ___
AB
3. CDA and CEA are right angles.
4. CDA and CEA are right triangles.
5. ___
AC ___
AC
6. ___
AE ___
CD
7. ACE CAD (HL HL)
9 1. ___
AE ___
BC
2. ___
CD ___
AB
3. AEB and CDB are right angles.
4. AEB and CDB are right triangles.
5. ___
DB ___
EB
6. DBE DBE
7. AEB CDB (Leg–acute angle)
8. ___
AE ___
CD (CPCTC)
10 1. ___
BD ___
AC
2. ___
QS ___
PR
3. BDA and QSP are right angles.
4. BDA and QSP are right triangles.
5. ABC PQR
6. ___
AB ___
PQ (CPCTC)
7. A P (CPCTC)
8. BDA QSP (Hypotenuse–
acute angle)
9. ABD PQS (CPCTC)
10. mABD mPQS
11. ___
BD bisects ABC.
12. 1 _ mABC mABD mPQS
2
13. 1 _ mABC
2 1 _ mPQR (Division
2
postulate)
14. mPQS 1 _ mPQR (Transitive
2
postulate)
15. ___
QS bisects PQR. (Definition of
angle bisector)
11 1. ___
AB ___
CF , ___
DE ___
CF
2. ABF and CED are right angles.
3. ABF and CED are right triangles.
4. ___
CD ___
AF
5. ___
BE ___
BE
6. ___
CE ___
FB
7. ABF CED (HL HL)
AB ___
DE
8. ___
9-8 Proving Right Triangles Congruent by Hypotenuse-Leg; Concurrence of Angle Bisectors of a Triangle 51