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ΔCAT = ΔDOG 45˚ Find the measure of angle C C A T D O G 45˚ 95˚ 40˚ 5 7 9 2x + 1

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Δ CAT = Δ DOG. O. 7. C. G. 95˚. 40˚. 2x + 1. 5. 9. 4 5˚. A. T. D. Find the measure of angle C. 45˚. Why are the triangles congruent?. ASA. The perimeter of Δ HAT is 110. HA = x + 5, AT = 2x – 25, and HT 40. Is Δ HAT scalene, isosceles, or equilateral?. - PowerPoint PPT Presentation

### Transcript of Δ CAT = Δ DOG 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 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