Δ cat = Δ dog
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ΔCAT = ΔDOG
45˚
Find the measure of angle C
C
A T D
OG
45˚
95˚40˚
5
7
92x +
1
Why are the triangles congruent?
ASA
The perimeter of ΔHAT is 110. HA = x + 5, AT = 2x – 25, and HT 40. Is ΔHAT scalene, isosceles, or equilateral?
x + 5 + 2x – 25 + 40 = 110 3x + 20 = 110
3x = 90 x = 30
The sides are 40, 35 and 35, so isosceles.
Find the measure of angle 1 and angle 2. Rays AC and AD trisect angle BAE.
Angle 1 = 93˚Angle 2 = 81˚
B C D E
A
12
6˚
Always, Sometimes, or Never?
Always
An altitude of a triangle is perpendicular to the side to which it is drawn.
ΔMLK = ΔCOW
3x + 3 = 18 3x = 15 x = 5
Find the value of x.
L
M
K
WO
C
30˚50˚
100˚
15
18
123x + 3
Always, Sometimes, or Never?
Never
A right triangle is obtuse.
Always, Sometimes, or Never?
Sometimes
An obtuse triangle is isosceles
Always, Sometimes, or Never?
Never
An equilateral triangle is right.
The perimeter of ΔAND is 69. AN = 23, ND = 3x + 2 and DA = 5x - 12 Is ΔAND scalene, isosceles, or equilateral?
23 + 3x + 2 + 5x – 12 = 69 8x +13 = 69
8x = 56 x = 7
The sides are 23, 23, and 23 so equilateral.
Always, Sometimes, or Never?
Sometimes
An altitude of a triangle bisects the side to which it is drawn.
ΔMLK = ΔCOW
50˚Find the measure of angle L.
L
M
K
WO
C
30˚50˚
100˚
15
18
123x + 3
Always, Sometimes, or Never?
Never
A median of a triangle is outside the triangle.
Always, Sometimes, or Never?
Sometimes
An altitude of a triangle is outside the triangle.
Always, Sometimes, or Never?
Sometimes
The base angles of an isosceles triangle are larger than the vertex angle.
Find the measure of angle 1 and angle 2. Rays AC and AD trisect angle BAE.
Angle 1 = 96˚Angle 2 = 72˚
B C D E
A
12
12˚
Why are the triangles congruent?
Not congruent(angle, side, side)
Always, Sometimes, or Never?
Always
2 triangles are congruent if 3 pairs of corresponding sides are congruent.
Why are the triangles congruent?
Not congruent(angle, angle, angle)
Always, Sometimes, or Never?
Sometimes
An obtuse triangle is scalene.
Why are the triangles congruent?
SAS
A
B C
DΔABC & ΔDCB
Always, Sometimes, or Never?
Always
2 right triangles are congruent if their hypotenuses and a pair of acute angles are congruent.
Why are the triangles congruent?
SAS
Always, Sometimes, or Never?
Sometimes
2 triangles are congruent if 2 pairs of corresponding sides, and a pair of non-included angles are congruent.
Find the measure of angle 1 and angle 2. Rays AC and AD trisect angle BAE.
Angle 1 = 80˚Angle 2 = 60˚
B C D E
A
12
20˚
Always, Sometimes, or Never?
Never
A right triangle is acute.
The perimeter of ΔBUG is 36. BU = 12, BG = 2x + 2, and UG = 3x – 3. Is ΔBUG scalene, isosceles, or equilateral?
12 + 2x + 2 + 3x – 3 = 36 5x + 11 = 36
5x = 25 x = 5
The sides are 12, 12, and 12, so equilateral
Always, Sometimes, or Never?
Always
An equilateral triangle is acute.
ΔCAT = ΔDOG
2x + 1 = 5 2x = 4 x = 2
Find the value of x.
C
A T D
OG
45˚
95˚40˚
5
7
92x +
1
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