Δ CAT = Δ DOG

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# Δ CAT = Δ DOG - PowerPoint PPT Presentation

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?.

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ΔCAT = ΔDOG

O

7

C

G

95˚

40˚

2x + 1

5

9

45˚

A

T

D

Find the measure of angle C

45˚

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.

A

1

2

B

C

D

E

Angle 1 = 93˚

Angle 2 = 81˚

Always, Sometimes, or Never?

An altitude of a triangle is perpendicular to the side to which it is drawn.

Always

ΔMLK = ΔCOW

W

M

3x + 3

O

30˚

12

50˚

15

100˚

L

18

K

C

Find the value of x.

3x + 3 = 18

3x = 15

x = 5

Always, Sometimes, or Never?

A right triangle is obtuse.

Never

Always, Sometimes, or Never?

An obtuse triangle is isosceles

Sometimes

Always, Sometimes, or Never?

An equilateral triangle is right.

Never

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?

An altitude of a triangle bisects the side to which it is drawn.

Sometimes

ΔMLK = ΔCOW

W

M

3x + 3

O

30˚

12

50˚

15

100˚

L

18

K

C

Find the measure of angle L.

50˚

Always, Sometimes, or Never?

A median of a triangle is outside the triangle.

Never

Always, Sometimes, or Never?

An altitude of a triangle is outside the triangle.

Sometimes

Always, Sometimes, or Never?

The base angles of an isosceles triangle are larger than the vertex angle.

Sometimes

Find the measure of angle 1 and angle 2. Rays AC and AD trisect angle BAE.

A

12˚

1

2

B

C

D

E

Angle 1 = 96˚

Angle 2 = 72˚

Why are the triangles congruent?

Not congruent

(angle, side, side)

Always, Sometimes, or Never?

2 triangles are congruent if 3 pairs of corresponding sides are congruent.

Always

Why are the triangles congruent?

Not congruent

(angle, angle, angle)

Always, Sometimes, or Never?

An obtuse triangle is scalene.

Sometimes

Always, Sometimes, or Never?

2 right triangles are congruent if their hypotenuses and a pair of acute angles are congruent.

Always

Always, Sometimes, or Never?

2 triangles are congruent if 2 pairs of corresponding sides, and a pair of non-included angles are congruent.

Sometimes

Find the measure of angle 1 and angle 2. Rays AC and AD trisect angle BAE.

A

20˚

1

2

B

C

D

E

Angle 1 = 80˚

Angle 2 = 60˚

Always, Sometimes, or Never?

A right triangle is acute.

Never

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?

An equilateral triangle is acute.

Always

ΔCAT = ΔDOG

O

7

C

G

95˚

40˚

2x + 1

5

9

45˚

A

T

D

Find the value of x.

2x + 1 = 5

2x = 4

x = 2