Triangle Congruence: SSS and HL (Assignment)

To prove that ΔDEF ≅ ΔDGF by SSS, what additional information is needed?

DE ≅ DG

In the diagram, BC ≅ EF and ∠A and ∠D are right angles.

For the triangles to be congruent by HL, what must be the value of x?

x=8

M is the midpoint of AD.

What value of x will make triangles ABM and DCM congruent?

x=7

M is the midpoint of AD

What single transformation is required to map one of these congruent triangles onto the other?

Reflection

Isosceles triangle ABC is folded along BM with M chosen in such a way that it is the midpoint of side AC, the shortest side.

1. Which pair of sides are congruent based on the definition of midpoint?
2. Which pair of sides are congruent based on the reflexive property?
3. Which pair of sides are congruent based on the definition of isosceles triangles?

1. AM and CM
2. BM and BM
3. AB and CB

The triangles are congruent by the SSS congruence theorem.

Which transformation(s) can map ΔLMN onto ΔL'M'N'?

Rotation then Translation

The four-sided geometric figure pictured is called a parallelogram. One feature of parallelograms is that opposite sides have equal lengths.

The dotted line splits the parallelogram into two triangles.

What is true about the congruency of the two triangles?

The triangles can be proven congruent using SSS.

The two triangles created by the diagonal of the parallelogram are congruent. Recall that the opposite sides of a parallelogram are congruent.

Which transformation(s) could map one triangle to the other?

Rotation and Translation

AB ≅ BC and AD ≅ CD

1. What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
2. What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?

1. AC and BD are Perpendicular
2. AX and CX are Congruent