Triangle Congruence: SSS and HL Assignment and Quiz

The triangles shown are congruent by the SSS congruence theorem. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations?

rotation, then translation, then reflection

The triangles are congruent by the SSS congruence theorem. Which transformation(s) can map BCD onto WXY?

translation, then rotation

Which shows two triangles that are congruent by the SSS congruence theorem?

D

Triangle DEF and triangle DGF are shown in the diagram. To prove that ΔDEF ≅ ΔDGF by SSS, what additional information is needed?

DE ≅ DG

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

AM and CM BM and BM AB and CB

Which explains whether ΔFGH is congruent to ΔFJH?

They are not congruent because only one pair of corresponding sides is congruent.

The triangles are congruent by SSS and HL. Which transformation(s) can be used to map △RST onto △VWX?

rotation, then translation

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

reflection

Triangle ABC is congruent to A'BC' by the HL theorem. What single rigid transformation maps ABC onto A'BC'?

reflection

The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map ABC onto FED?

reflection, then translation

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

The triangles are congruent by SSS or HL. Which transformation(s) can map MNQ onto PQN?

rotation, then translation

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

4

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?

8

Point H is the midpoint of side FK. For the triangles to be congruent by SSS, what must be the value of x?

6

AB ≅ BC and AD ≅ CD What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem? What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?

AC and BD are perpendicular AX and CX are congruent

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.

M is the midpoint of AD. What value of x will make triangles ABM and DCM congruent?

7

The triangles are congruent by the SSS congruence theorem. Which transformation(s) can map ΔLMN onto ΔL'M'N'?

rotation then translation