Download Geometry Name Manning Unit 3 Test Review: Part 1 Identify each

Geometry
Manning
Name _________________________________
Unit 3 Test Review: Part 1
Identify each statement as true or false. Justify your answer (true or false) by either using a conjecture or a
clear explanation that can (but doesn’t have to) include a labeled diagram.
1) If one of the base angles of an isosceles triangle is 22°, then the vertex angle has a measure of 156°?
True. Base angles are congruent, so the other base angle is also 22 degrees. All the angles
inside the triangle must add to 180 degrees, and 22+22+156=180.
2) One triangle has two sides that are congruent to two sides in another triangle. The triangles also have a
non-included angle that is congruent to the non-included angle in the other triangle. The two triangles
must be congruent to each other.
False. SSA does not prove that two triangles are congruent to each other. More information is
needed to prove congruence.
3) The sum of interior angles in some triangles is greater than the sum of triangles in other triangles.
False. The sum of the interior angles for ALL triangles is 180 degrees. No exceptions.
4) Calculate the measure of each lettered angle.
a = 112° (Linear pair)
b = 68° (Alternate Interior)
c = 44° (180° make a line)
d = 44° (Alternate Interior)
e = 136° (Linear pair)
f = 68° (Isosceles Base Angles)
g = 68° (Isosceles Base Angles)
h = 56° (Isosceles Base Angles)
k = 68° (180 – c - g)
l = 56° (180 – k – h)
m = 124° (Alt. Int. to h+k)
Geometry
Name _________________________________
Manning
5) Describe why lengths 3cm, 8cm and 14 cm cannot form a triangle. Include a diagram that shows the three
segments NOT forming a triangle.
3cm + 8cm < 14cm
The two smaller segments must add up (sum) to MORE than the longest segment.
6)
mT  (180°-28°)/2 = 76°
RA  5cm (RA is congruent to TA)
7)
Write an equation and use it to determine y. Show your algebra work.
𝟑𝟓° + 𝟑𝐲° + (𝐲 − 𝟏𝟔)° = 𝟏𝟖𝟎°
𝟒𝒚° + 𝟏𝟗° = 𝟏𝟖𝟎°
𝟒𝒚° = 𝟏𝟔𝟏°
8) Arrange the letters in order from greatest value to least value. What conjecture do you need to use to
solve this?
c>b>a
c is opposite from the greatest angle (We know because the opposite angle is 90 degrees)
b is opposite from the middle angle (We know because 180°-30°-90° = 60°)
a is opposite from the smallest angle (We know because 30° is smaller than 60° and 90°)
Geometry
Manning
Name _________________________________
Name 2 congruent triangles, if possible, and give the conjecture that you can use to prove that they are congruent.
Write “can’t be determined” or “need more information” if it is not possible to determine that the triangles are
congruent with the information you are given and can infer.
1)
∆𝑨𝑪𝑩 ≅ ∆𝑫𝑪𝑬 Or Equivalent Congruence Statement
Reason: SAS, because ∠𝑩𝑪𝑨 ≅ ∠𝑬𝑪𝑫 (vertical pair of angles)
2)
∆𝑹𝑻𝑼 ≅ ∆𝑹𝑻𝑺 Or Equivalent Congruence Statement
Reason: AAS, because ̅̅̅̅
𝑹𝑻 ≅ ̅̅̅̅
𝑹𝑻 (reflexive property)
3) KI bisects angle JIH.
∆𝑲𝑰𝑯 ≅ ∆𝑲𝑰𝑱 Or Equivalent Congruence Statement
̅̅̅̅ ≅ 𝑲𝑰
̅̅̅̅ (reflexive property)
Reason: SAS, because ∠𝑯𝑲𝑰 ≅ ∠𝑱𝑲𝑰 (definition of angle bisector) and 𝑲𝑰
4) ZA is a median and a perpendicular bisector.
∆𝒁𝑨𝑿 ≅ ∆𝒁𝑨𝒀 Or Equivalent Congruence Statement
Reason: SAS, because ∠𝒁𝑨𝑿 ≅ ∠𝒁𝑨𝒀 (all right angles are congruent) and
̅̅̅̅ ≅ 𝒁𝑨
̅̅̅̅ (reflexive property), and 𝑿𝑨
̅̅̅̅ ≅ 𝒀𝑨
̅̅̅̅(definition of perpendicular bisector)
𝒁𝑨