Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
Page 1
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1 Given:
and
Prove:
and
intersect at point C
are drawn
2 In the diagram below,
.
Prove:
3 In the diagram of
Prove:
below,
and medians
and
are drawn.
Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
Page 2
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Name: __________________________________
4 Complete the partial proof below for the accompanying diagram by providing reasons for
steps 3, 6, 8, and 9.
Given:
Prove:
,
Statements
1
2
,
,
,
Reasons
1 Given
2 Given
3
and
are
right angles.
3
4
5
6
4 All right angles
are congruent.
5 Given
6
7
8
7 Given
8
9
9
,
Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
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Name: __________________________________
5 Given:
Prove:
,
,
with
is the perpendicular bisector of
, and
Fill in the missing statement and reasons below.
Statements
,
,
1
with
,
and
2
3
and
are supplementary.
and
are supplementary.
4
5
6
,
7
is the
perpendicular
bisector of
.
Reasons
1 Given
2
3 Linear pairs of
angles are
supplementary.
4 Supplements of
congruent angles
are congruent.
5 ASA
6
7
Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
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6 Given:
Prove:
,
bisects
7 Given:
bisects
,
at E.
Prove:
8 Given:
Prove:
and
, C is the midpoint of
and
Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
Page 5
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Name: __________________________________
9 Given:
and
and
bisect each other at point X
are drawn
Prove:
10 Given:
Prove:
and
intersect at B,
, and
bisects
.
Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
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1 ANS:
and
intersect at point C,
(Vertical Angles).
,
(SAS).
,
and
are drawn (Given).
REF: 011529ge
2 ANS:
(given);
(CPCTC);
(CPCTC);
(segment subtraction);
REF: 081933geo
3 ANS:
,
and medians
and
are given.
isosceles triangle (definition of isosceles triangle).
midpoint of
and T is the midpoint of
(definition of midpoint).
(CPCTC).
(vertical angles are congruent);
(AAS)
(reflexive property).
is an
(isosceles triangle theorem). B is the
(definition of median).
(multiplication postulate).
and
(SAS).
REF: 061338ge
4 ANS:
3 Perpendicular line segments form right angles; 6 If two parallel lines are cut by a transversal, the
alternate interior angles are congruent; 8 AAS; 9 CPCTC.
REF: 060229b
5 ANS:
2 Reflexive; 4
; 6 CPCTC; 7 If points B and D are equidistant from the endpoints of
, then B and D are on the perpendicular bisector of
.
REF: 081832geo
6 ANS:
,
bisects
,
(Reflexive property).
and
(All right angles are congruent).
REF: 081335ge
7 ANS:
,
(Given).
(Definition of angle bisector).
are right angles (Definition of perpendicular).
(SAS).
(CPCTC).
Regents Exam Questions G.SRT.B.5: Triangle Proofs 2
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and
are right angles because perpendicular lines form right angles.
angles are congruent.
because vertical angles are congruent.
ASA.
because CPCTC.
because all right
because of
REF: 061235ge
8 ANS:
and
and
because of the definition of midpoint.
because of vertical angles.
because of SAS.
because of CPCTC.
is a transversal intersecting
. Therefore
because
and
are congruent alternate interior angles.
REF: 060938ge
9 ANS:
and
bisect each other at point X;
and
are drawn (given);
and
(segment
bisectors create two congruent segments);
(vertical angles are congruent);
(SAS);
(CPCTC);
(a transversal that creates congruent alternate interior angles cuts
parallel lines).
REF: 061733geo
10 ANS:
and
intersect at B,
, and
(Alternate Interior Angles).
segments).
(ASA).
REF: 081435ge
bisects
(Given).
(Vertical Angles).
(The bisection of a line segment creates two congruent
(CPCTC).