Triangle Congruency

How are these triangles congruent?

• HL

• SSA

• SSS

• CPCTC

• SAS

Answer explanation

There are 3 sides that are congruent to each other. Therefore, you can use the (S)ide (S)ide (S)ide postulate to prove the triangles congruent.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

How are these triangles congruent?

• SSS

• SAS

• AAS

• ASA

• HL

Answer explanation

There are two congruent sides and one congruent angle in between. So, you can use the (S)ide (A)ngle (S)ide postulate to prove both of the triangles are congruent.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

How are these triangles congruent?

• SAS

• SSS

• AAS

• SSA

• ASA

Answer explanation

There are 2 congruent angles with one congruent side in between. The side is congruent because of the reflexive property, where it is congruent to itself. You can then prove the two triangles congruent by using the (A)ngle (S)ide (A)ngle postulate.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

How are these triangles congruent?

• HL

• CPCTC

• AAS

• SAS

• ASA

Answer explanation

There are two congruent angles and then one congruent side (in that order). The side is congruent because of the reflexive property, where it is congruent to itself. Then, you can use the (A)ngle (A)ngle (S)ide postulate to prove the two triangles congruent.

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

How are these triangles congruent?

• SSS

• HL

• ASA

• AAS

• SAS

Answer explanation

The (H)ypotenuse (L)eg postulate states that if a leg and hypotenuse of a right triangle are congruent, then the two triangles are congruent. This example fits into those criteria, and you cannot make any other triangle with those conditions. So, you can use the (H)ypotenuse (L)eg postulate to prove the two triangles congruent.

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CPCTC stands for Corresponding Parts of Congruent _________ are Congruent

(Capitalize your answer)

Answer explanation

CPCTC stands for: (C)orresponding (P)arts of (C)ongruent (T)riangles are (C)ongruent

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.CO.C.10

Find the value for x.

Answer explanation

You can prove these triangles are congruent because all three sides are congruent, so you can use the SSS postulate. Because they are congruent, line segment AB corresponds with line segment DE. Using this, you can state that 2x - 5 = 15. You can simplify this expression into 2x = 20, and solve for x by dividing by 2, which is x = 10.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Find the value for x.

Answer explanation

These triangles are congruent by SAS. So, line segment BC is corresponding with line segment EF. With this, you can state that 1/4x + 1 = 3. Simplify it into 1/4x = 2, and then you get x = 8.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Find the length of line segment AB.

• 20

• 18

• 25

• 27

• Can't Prove Congruent

Answer explanation

These triangles are congruent by ASA. The first step to solving for line segment AB is by finding the value of x. We can see that BC corresponds with EF, so we can state that 12 = 2x, which simplifies to x = 6. Then, you can plug that in for the equation for line segment AB. 3(6) + 7 = 25. Line segment AB is 25 units long.

Tags

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

Find the length of line segment AC

Answer explanation

These triangles are congruent by AAS. To find the length of line segment AC, need to find x first. If you look at the corresponding line segments BC and EF, you can make a statement to find x: 2x + 5 = 21. You can simplify this into 2x = 16, which equals x = 8. Then, we can plug that into the equation for the line segment AC: 3(8) + 2 = 26

Tags

CCSS.HSG.SRT.B.5

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

CCSS.HSG.SRT.D.11