Download Chapter_4_Review

Honors Geometry
Ch 4 Review Practice
Name______________________________________#_______
Some practice proofs.
DA bisects BAC
Given:
A.
AD  BC
B  C
Show:
A
1 3
2 4
D
B
B.
Given:
C
FS // LG
LS // AG
L is the midpoint of FA
LS  AG
Show:
F
L
3
S
2
A
C.
G
H and N are right angles
Given:
DO  OU
HD  NU
Show:
U
H
D
O
2
1
N
All of the following statements are false. Correct them to make them true.
1. The sum of the measures of the angles in an obtuse triangle is greater than the sum of the
measures of the angles in scalene triangle.
2. In an isosceles triangle, if the measure of one base angle is 45 degrees, then the triangle must be an
acute triangle.
3. In right scalene triangle ABC with right angle B, if 𝒎∠𝑨 = 𝟔𝟕° then ̅̅̅̅
𝑩𝑪 is the shortest side.
4. If a triangle has two 30 degree angles, then it is an acute isosceles triangle.
5. If the measure of an exterior angle of a triangle is twice its linear pair, then the sum of the two
remote interior angles is 90 degrees.
6. If two sides of one triangle are congruent to two sides of another triangle then the triangles must
be congruent.
7. Only one triangle can be constructed from two sides and a non-included angle.
8. In a right triangle, the bisector of the right angle is also an altitude.
9. Every equilateral triangle is equiangular, but not every equiangular triangle is equilateral.
10. CPCTC stands for Congruent Parts of Congruent Triangles are Corresponding.
11. If a point is equidistant from the endpoints of a segment, then it must be the midpoint of the
segment.
12. If two parallel lines are cut by a transversal, then the consecutive interior angles are congruent.
13. If two lines do not intersect, they must be parallel.
14. Deductive reasoning involves recognizing patterns.
15. You use a ruler and a protractor to do geometric constructions.
16. In triangle XYZ, if 𝒎∠𝑿 = 𝟑𝟓° 𝒂𝒏𝒅 𝒎∠𝒁 = 𝟏𝟎𝟎°, list the sides in order from shortest to longest.
1.
Given WER  CHS , complete the congruence statements:
SC  ________
EW  ________
H  ________
ER  ________
C  ________
R  ________
2.
Determine if the given lengths can create a triangle. You must show why or why not.
a.)
81 47
,
, 27
4 4
b.)
c.)
26
1
, 4, 10
5
5
15, 9, 24
5.
If two sides of a triangle measure 78 cm and 31 cm, between what two numbers must the measure of the
3rd side fall?
6.
Given RED where mR  141 ,
mE  30 , mD  9 , list the sides of the
triangle from longest to shortest.
8.
The perimeter of the triangle is 142 cm, find all the missing measures in the diagram.
7.
Given BLU where BL  19 cm ,
LU  65 cm , BU  48 cm , list the angles of
the triangle from the smallest to largest.
Solve for variable(s) in each picture.
9.
________
10.
________
11.
________
◦
(x+5)
◦
(3x - 10)
◦
(115)
12.
________
13.
________
14.
________
15.
________
16.
________
17.
________
18.
________
19.
________ & ________
20.
________
21.
TRY  GEO , mT  36 , mE  73 , Find mO .
22.
Given: ABC  XYZ, AB  38 , YZ  28 , and XY   5x  8 . Solve for x . (Hint: Draw a picture.)
23.
Given an isosceles triangle with vertex angle that measures 70, what is the measure of a base angle?
24.
25.
Given: ABC is isosceles with vertex C. If mA   3x  6  and mC   2 x  . Solve for x and
find mB . (Hint: Draw a picture.)
ABC is an isosceles triangle with vertex angle B. AB = 5x – 28, AC = x+ 5, and BC = 2x + 11.
Solve for x and find the length of the base. (Hint: Draw a picture.)
Determine if the given triangles are congruent. If yes, state the reason why.
26.
________
27.
________
28.
________
29.
________
30.
________
31.
________
32.
________
33.
________
34. Construct triangle ABC given the following side and angles:
•
A
•
B
A
B
35. Construct the incenter of the triangle below.